MTH402 tutorial pdf | Campusflava https://campusflava.com Tutors, Past Questions and Projects. Tue, 22 Feb 2022 17:38:09 +0000 en-US hourly 1 https://wordpress.org/?v=6.6.3 https://i0.wp.com/campusflava.com/wp-content/uploads/2023/01/cropped-CF.png?fit=32%2C32&ssl=1 MTH402 tutorial pdf | Campusflava https://campusflava.com 32 32 123014824 MTH402 Solutions https://campusflava.com/blog/mth402-solutions-2/ https://campusflava.com/blog/mth402-solutions-2/#respond Sun, 09 Jan 2022 16:29:16 +0000 https://campusflava.com/blog/mth402-solutions-2/ MTH402 Tma Solutions 1. Let X be a topological space. Then one of the following conditions does not hold \(\phi\) and X are closed Arbitrary intersection of closed sets is closed —>> Infinite unions of closed sets are closed Finite unions of closed sets are closed 2. Let \(\mathbb R\) be with the usual standard […]

The post MTH402 Solutions first appeared on Campusflava.]]> MTH402 Tma Solutions

1. Let X be a topological space. Then one of the following conditions does not hold

\(\phi\) and X are closed

Arbitrary intersection of closed sets is closed

—>> Infinite unions of closed sets are closed

Finite unions of closed sets are closed

2. Let \(\mathbb R\) be with the usual standard topology and let A \subsets \mathbb R\).Then A is open in \(\mathbb R\) if there exists an interval I such that I\subset A. For a,b\(\epsilon\mathbb R, I =

—>> I = ( a, b)

I = ( a, b]

I = [ a,b]

I = [a,b)

3. A set is nowhere dense if the set \(bar {A}\) has empty ____________
Inferior
Accumulation point
—>> Interior
Exterior
4. When is \(B\) aneuclidean topology \(\mathbb R?\) When
\(\mathbb B = (a,b): a,b\epsilon\mathbb R, a=b\)
\(\mathbb B = (a,b): a,b\epsilon\mathbb R, a>b\)
—>> \(\mathbb B = (a,b): a,b\epsilon\mathbb R, a<b\)
\(\mathbb B = (a,b): a,b\epsilon\mathbb R, a/b\)
5. Let X be a set. A topology on X is acollection \(\tau \)of subsets of X, for which one of these does not hold:
The set X itself and the empty set \(\phi\) are in \(\tau\)
Arbitrary unions\( \bigcup_{}^{}\cup\) of elememnts of \(\tau\) are in \(\tau\)
Finite intersection \(\bigcap\cup_k\) of elements of \(\tau\) are in \(\tau\)
—>> The set X x X is also a member of \(\chi\)
6. A set \(\bigcup\) is open in the meric topology induced by d if and only for each x\(\epsilon\bigcup\), there exist \(\epsilon> 0\) such that
—>> B_d( x,\(\epsilon)\subset\bigcup\)
\(B_d( x,\epsilon)\supset\bigcup\)
\(B_d( x,\epsilon) = \bigcup\)
\(B_d( x,\epsilon)\) > \bigcup\)
7. The countable collection B = { ( a, b ) : a<b, a,b\(\epsilon\mathbb Q\)} is a ___________________________ for a topology on \(\mathbb R\)
Platform
Nucleus
—>> Basis
Reason
8. Let \(\pi_{1}( x, y) =x\) and \(\pi_{2}( x,y) =y \)then \(\pi_{1} : X x Y\rightarrow X \)and \(\pi_{2} : X x X\rightarrow\) Y. The maps \(\pi_{1}\) and \(\pi_{2}\) are called ____________________________
—>> Projections of X x X
Projections of X x X
Projections of Y x Y
projections of X^2 x Y^2
9. \(B\) is the lower limit topology on \(\mathbb R\) if
—>> \(\mathbb B’ = {[a,b) : a,b\epsilon\mathbb R; a<b}\)
\(\mathbb B’ = {(a,b] : a,b\epsilon\mathbb R; a<b}\)

\(\mathbb B’ = {[a,b] : a,b\epsilon\mathbb R; a<b}\)

\(\mathbb B’ = (a,b) : a,b\epsilon\mathbb R; a<b\)

10. A metric on a set X with a function d : X x X \(\rightarrow\mathbb R\) holds for all but one property in the following:

d(x,y)\(\geq 0\forall x,y\epsilon X\)

\(d(x,y) = d(y,m)\forall x,y\epsilon X\)

\(d(x,y)\leq d(x,y) + d(y,z)\forall x,y,z\epsilon X\)

—>> \(d(x,y) = 0 \)whenever \(\neq\) and \(x,y\epsilon X\)

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The post MTH402 Solutions first appeared on Campusflava.]]> https://campusflava.com/blog/mth402-solutions-2/feed/ 0 70559 A metric on a set X with a function d : X x X \(\rightarrow\mathbb R\) holds for all but one property in the following: https://campusflava.com/blog/a-metric-on-a-set-x-with-a-function-d-x-x-x-rightarrowmathbb-r-holds-for-all-but-one-property-in-the-following-2/ https://campusflava.com/blog/a-metric-on-a-set-x-with-a-function-d-x-x-x-rightarrowmathbb-r-holds-for-all-but-one-property-in-the-following-2/#respond Sun, 09 Jan 2022 16:25:43 +0000 https://campusflava.com/blog/a-metric-on-a-set-x-with-a-function-d-x-x-x-rightarrowmathbb-r-holds-for-all-but-one-property-in-the-following-2/ A metric on a set X with a function d : X x X \(\rightarrow\mathbb R\) holds for all but one property in the following: d(x,y)\(\geq 0\forall x,y\epsilon X\) \(d(x,y) = d(y,m)\forall x,y\epsilon X\) \(d(x,y)\leq d(x,y) + d(y,z)\forall x,y,z\epsilon X\) —>> \(d(x,y) = 0 \)whenever \(\neq\) and \(x,y\epsilon X\)

The post A metric on a set X with a function d : X x X \(\rightarrow\mathbb R\) holds for all but one property in the following: first appeared on Campusflava.]]> A metric on a set X with a function d : X x X \(\rightarrow\mathbb R\) holds for all but one property in the following:

d(x,y)\(\geq 0\forall x,y\epsilon X\)

\(d(x,y) = d(y,m)\forall x,y\epsilon X\)

\(d(x,y)\leq d(x,y) + d(y,z)\forall x,y,z\epsilon X\)

—>> \(d(x,y) = 0 \)whenever \(\neq\) and \(x,y\epsilon X\)

The post A metric on a set X with a function d : X x X \(\rightarrow\mathbb R\) holds for all but one property in the following: first appeared on Campusflava.]]> https://campusflava.com/blog/a-metric-on-a-set-x-with-a-function-d-x-x-x-rightarrowmathbb-r-holds-for-all-but-one-property-in-the-following-2/feed/ 0 70558 \(B\) is the lower limit topology on \(\mathbb R\) if https://campusflava.com/blog/b-is-the-lower-limit-topology-on-mathbb-r-if-2/ https://campusflava.com/blog/b-is-the-lower-limit-topology-on-mathbb-r-if-2/#respond Sun, 09 Jan 2022 16:25:36 +0000 https://campusflava.com/blog/b-is-the-lower-limit-topology-on-mathbb-r-if-2/ \(B\) is the lower limit topology on \(\mathbb R\) if —>> \(\mathbb B’ = {[a,b) : a,b\epsilon\mathbb R; a<b}\) \(\mathbb B’ = {(a,b] : a,b\epsilon\mathbb R; a<b}\) \(\mathbb B’ = {[a,b] : a,b\epsilon\mathbb R; a<b}\) \(\mathbb B’ = (a,b) : a,b\epsilon\mathbb R; a<b\)

The post \(B\) is the lower limit topology on \(\mathbb R\) if first appeared on Campusflava.]]> \(B\) is the lower limit topology on \(\mathbb R\) if

—>> \(\mathbb B’ = {[a,b) : a,b\epsilon\mathbb R; a<b}\)

\(\mathbb B’ = {(a,b] : a,b\epsilon\mathbb R; a<b}\)

\(\mathbb B’ = {[a,b] : a,b\epsilon\mathbb R; a<b}\)

\(\mathbb B’ = (a,b) : a,b\epsilon\mathbb R; a<b\)

The post \(B\) is the lower limit topology on \(\mathbb R\) if first appeared on Campusflava.]]> https://campusflava.com/blog/b-is-the-lower-limit-topology-on-mathbb-r-if-2/feed/ 0 70557 Let \(\pi_{1}( x, y) =x\) and \(\pi_{2}( x,y) =y \)then \(\pi_{1} : X x Y\rightarrow X \)and \(\pi_{2} : X x X\rightarrow\) Y. The maps \(\pi_{1}\) and \(\pi_{2}\) are called ____________________________ https://campusflava.com/blog/let-pi_1-x-y-x-and-pi_2-xy-y-then-pi_1-x-x-yrightarrow-x-and-pi_2-x-x-xrightarrow-y-the-maps-pi_1-and-pi_2-are-called-____-2/ https://campusflava.com/blog/let-pi_1-x-y-x-and-pi_2-xy-y-then-pi_1-x-x-yrightarrow-x-and-pi_2-x-x-xrightarrow-y-the-maps-pi_1-and-pi_2-are-called-____-2/#respond Sun, 09 Jan 2022 16:25:28 +0000 https://campusflava.com/blog/let-pi_1-x-y-x-and-pi_2-xy-y-then-pi_1-x-x-yrightarrow-x-and-pi_2-x-x-xrightarrow-y-the-maps-pi_1-and-pi_2-are-called-____-2/ Let \(\pi_{1}( x, y) =x\) and \(\pi_{2}( x,y) =y \)then \(\pi_{1} : X x Y\rightarrow X \)and \(\pi_{2} : X x X\rightarrow\) Y. The maps \(\pi_{1}\) and \(\pi_{2}\) are called ____________________________ —>> Projections of X x X Projections of X x X Projections of Y x Y projections of X^2 x Y^2

The post Let \(\pi_{1}( x, y) =x\) and \(\pi_{2}( x,y) =y \)then \(\pi_{1} : X x Y\rightarrow X \)and \(\pi_{2} : X x X\rightarrow\) Y. The maps \(\pi_{1}\) and \(\pi_{2}\) are called ____________________________ first appeared on Campusflava.]]> Let \(\pi_{1}( x, y) =x\) and \(\pi_{2}( x,y) =y \)then \(\pi_{1} : X x Y\rightarrow X \)and \(\pi_{2} : X x X\rightarrow\) Y. The maps \(\pi_{1}\) and \(\pi_{2}\) are called ____________________________

—>> Projections of X x X

Projections of X x X

Projections of Y x Y

projections of X^2 x Y^2

The post Let \(\pi_{1}( x, y) =x\) and \(\pi_{2}( x,y) =y \)then \(\pi_{1} : X x Y\rightarrow X \)and \(\pi_{2} : X x X\rightarrow\) Y. The maps \(\pi_{1}\) and \(\pi_{2}\) are called ____________________________ first appeared on Campusflava.]]> https://campusflava.com/blog/let-pi_1-x-y-x-and-pi_2-xy-y-then-pi_1-x-x-yrightarrow-x-and-pi_2-x-x-xrightarrow-y-the-maps-pi_1-and-pi_2-are-called-____-2/feed/ 0 70556 The countable collection B = { ( a, b ) : a https://campusflava.com/blog/the-countable-collection-b-a-b-a-2/ https://campusflava.com/blog/the-countable-collection-b-a-b-a-2/#respond Sun, 09 Jan 2022 16:25:17 +0000 https://campusflava.com/blog/the-countable-collection-b-a-b-a-2/ The countable collection B = { ( a, b ) : a<b, a,b\(\epsilon\mathbb Q\)} is a ___________________________ for a topology on \(\mathbb R\) Platform Nucleus —>> Basis Reason

The post The countable collection B = { ( a, b ) : a first appeared on Campusflava.]]> The countable collection B = { ( a, b ) : a<b, a,b\(\epsilon\mathbb Q\)} is a ___________________________ for a topology on \(\mathbb R\)

Platform

Nucleus

—>> Basis

Reason

The post The countable collection B = { ( a, b ) : a first appeared on Campusflava.]]> https://campusflava.com/blog/the-countable-collection-b-a-b-a-2/feed/ 0 70555 A set \(\bigcup\) is open in the meric topology induced by d if and only for each x\(\epsilon\bigcup\), there exist \(\epsilon> 0\) such that https://campusflava.com/blog/a-set-bigcup-is-open-in-the-meric-topology-induced-by-d-if-and-only-for-each-xepsilonbigcup-there-exist-epsilon-0-such-that-2/ https://campusflava.com/blog/a-set-bigcup-is-open-in-the-meric-topology-induced-by-d-if-and-only-for-each-xepsilonbigcup-there-exist-epsilon-0-such-that-2/#respond Sun, 09 Jan 2022 16:25:09 +0000 https://campusflava.com/blog/a-set-bigcup-is-open-in-the-meric-topology-induced-by-d-if-and-only-for-each-xepsilonbigcup-there-exist-epsilon-0-such-that-2/ A set \(\bigcup\) is open in the meric topology induced by d if and only for each x\(\epsilon\bigcup\), there exist \(\epsilon> 0\) such that —>> B_d( x,\(\epsilon)\subset\bigcup\) \(B_d( x,\epsilon)\supset\bigcup\) \(B_d( x,\epsilon) = \bigcup\) \(B_d( x,\epsilon)\) > \bigcup\)

The post A set \(\bigcup\) is open in the meric topology induced by d if and only for each x\(\epsilon\bigcup\), there exist \(\epsilon> 0\) such that first appeared on Campusflava.]]> A set \(\bigcup\) is open in the meric topology induced by d if and only for each x\(\epsilon\bigcup\), there exist \(\epsilon> 0\) such that

—>> B_d( x,\(\epsilon)\subset\bigcup\)

\(B_d( x,\epsilon)\supset\bigcup\)

\(B_d( x,\epsilon) = \bigcup\)

\(B_d( x,\epsilon)\) > \bigcup\)

The post A set \(\bigcup\) is open in the meric topology induced by d if and only for each x\(\epsilon\bigcup\), there exist \(\epsilon> 0\) such that first appeared on Campusflava.]]> https://campusflava.com/blog/a-set-bigcup-is-open-in-the-meric-topology-induced-by-d-if-and-only-for-each-xepsilonbigcup-there-exist-epsilon-0-such-that-2/feed/ 0 70554 Let X be a set. A topology on X is acollection \(\tau \)of subsets of X, for which one of these does not hold: https://campusflava.com/blog/let-x-be-a-set-a-topology-on-x-is-acollection-tau-of-subsets-of-x-for-which-one-of-these-does-not-hold-2/ https://campusflava.com/blog/let-x-be-a-set-a-topology-on-x-is-acollection-tau-of-subsets-of-x-for-which-one-of-these-does-not-hold-2/#respond Sun, 09 Jan 2022 16:25:00 +0000 https://campusflava.com/blog/let-x-be-a-set-a-topology-on-x-is-acollection-tau-of-subsets-of-x-for-which-one-of-these-does-not-hold-2/ Let X be a set. A topology on X is acollection \(\tau \)of subsets of X, for which one of these does not hold: The set X itself and the empty set \(\phi\) are in \(\tau\) Arbitrary unions\( \bigcup_{}^{}\cup\) of elememnts of \(\tau\) are in \(\tau\) Finite intersection \(\bigcap\cup_k\) of elements of \(\tau\) are in […]

The post Let X be a set. A topology on X is acollection \(\tau \)of subsets of X, for which one of these does not hold: first appeared on Campusflava.]]> Let X be a set. A topology on X is acollection \(\tau \)of subsets of X, for which one of these does not hold:

The set X itself and the empty set \(\phi\) are in \(\tau\)

Arbitrary unions\( \bigcup_{}^{}\cup\) of elememnts of \(\tau\) are in \(\tau\)

Finite intersection \(\bigcap\cup_k\) of elements of \(\tau\) are in \(\tau\)

—>> The set X x X is also a member of \(\chi\)

The post Let X be a set. A topology on X is acollection \(\tau \)of subsets of X, for which one of these does not hold: first appeared on Campusflava.]]> https://campusflava.com/blog/let-x-be-a-set-a-topology-on-x-is-acollection-tau-of-subsets-of-x-for-which-one-of-these-does-not-hold-2/feed/ 0 70553 When is \(B\) a neuclidean topology \(\mathbb R?\) When https://campusflava.com/blog/when-is-b-a-neuclidean-topology-mathbb-r-when/ https://campusflava.com/blog/when-is-b-a-neuclidean-topology-mathbb-r-when/#respond Sun, 09 Jan 2022 16:24:52 +0000 https://campusflava.com/blog/when-is-b-a-neuclidean-topology-mathbb-r-when/ When is \(B\) a neuclidean topology \(\mathbb R?\) When \(\mathbb B = (a,b): a,b\epsilon\mathbb R, a=b\) \(\mathbb B = (a,b): a,b\epsilon\mathbb R, a>b\) —>> \(\mathbb B = (a,b): a,b\epsilon\mathbb R, a<b\) \(\mathbb B = (a,b): a,b\epsilon\mathbb R, a/b\)

The post When is \(B\) a neuclidean topology \(\mathbb R?\) When first appeared on Campusflava.]]> When is \(B\) a neuclidean topology \(\mathbb R?\) When

\(\mathbb B = (a,b): a,b\epsilon\mathbb R, a=b\)

\(\mathbb B = (a,b): a,b\epsilon\mathbb R, a>b\)

—>> \(\mathbb B = (a,b): a,b\epsilon\mathbb R, a<b\)

\(\mathbb B = (a,b): a,b\epsilon\mathbb R, a/b\)

The post When is \(B\) a neuclidean topology \(\mathbb R?\) When first appeared on Campusflava.]]> https://campusflava.com/blog/when-is-b-a-neuclidean-topology-mathbb-r-when/feed/ 0 70552 Let X be a topological space. Then one of the following conditions does not hold https://campusflava.com/blog/let-x-be-a-topological-space-then-one-of-the-following-conditions-does-not-hold-2/ https://campusflava.com/blog/let-x-be-a-topological-space-then-one-of-the-following-conditions-does-not-hold-2/#respond Sun, 09 Jan 2022 16:24:43 +0000 https://campusflava.com/blog/let-x-be-a-topological-space-then-one-of-the-following-conditions-does-not-hold-2/ Let X be a topological space. Then one of the following conditions does not hold \(\phi\) and X are closed Arbitrary intersection of closed sets is closed —>> Infinite unions of closed sets are closed Finite unions of closed sets are closed

The post Let X be a topological space. Then one of the following conditions does not hold first appeared on Campusflava.]]> Let X be a topological space. Then one of the following conditions does not hold

\(\phi\) and X are closed

Arbitrary intersection of closed sets is closed

—>> Infinite unions of closed sets are closed

Finite unions of closed sets are closed

The post Let X be a topological space. Then one of the following conditions does not hold first appeared on Campusflava.]]> https://campusflava.com/blog/let-x-be-a-topological-space-then-one-of-the-following-conditions-does-not-hold-2/feed/ 0 70551 Let \(\mathbb R\) be with the usual standard topology and let A \subsets \mathbb R\).Then A is open in \(\mathbb R\) if there exists an interval I such that I\subset A. For a,b\(\epsilon\mathbb R, I = https://campusflava.com/blog/let-mathbb-r-be-with-the-usual-standard-topology-and-let-a-subsets-mathbb-r-then-a-is-open-in-mathbb-r-if-there-exists-an-interval-i-such-that-isubset-a-for-abepsilon-2/ https://campusflava.com/blog/let-mathbb-r-be-with-the-usual-standard-topology-and-let-a-subsets-mathbb-r-then-a-is-open-in-mathbb-r-if-there-exists-an-interval-i-such-that-isubset-a-for-abepsilon-2/#respond Sun, 09 Jan 2022 16:24:31 +0000 https://campusflava.com/blog/let-mathbb-r-be-with-the-usual-standard-topology-and-let-a-subsets-mathbb-r-then-a-is-open-in-mathbb-r-if-there-exists-an-interval-i-such-that-isubset-a-for-abepsilon-2/ Let \(\mathbb R\) be with the usual standard topology and let A \subsets \mathbb R\).Then A is open in \(\mathbb R\) if there exists an interval I such that I\subset A. For a,b\(\epsilon\mathbb R, I = —>> I = ( a, b) I = ( a, b] I = [ a,b] I = [a,b)

The post Let \(\mathbb R\) be with the usual standard topology and let A \subsets \mathbb R\).Then A is open in \(\mathbb R\) if there exists an interval I such that I\subset A. For a,b\(\epsilon\mathbb R, I = first appeared on Campusflava.]]> Let \(\mathbb R\) be with the usual standard topology and let A \subsets \mathbb R\).Then A is open in \(\mathbb R\) if there exists an interval I such that I\subset A. For a,b\(\epsilon\mathbb R, I =

—>> I = ( a, b)

I = ( a, b]

I = [ a,b]

I = [a,b)

The post Let \(\mathbb R\) be with the usual standard topology and let A \subsets \mathbb R\).Then A is open in \(\mathbb R\) if there exists an interval I such that I\subset A. For a,b\(\epsilon\mathbb R, I = first appeared on Campusflava.]]> https://campusflava.com/blog/let-mathbb-r-be-with-the-usual-standard-topology-and-let-a-subsets-mathbb-r-then-a-is-open-in-mathbb-r-if-there-exists-an-interval-i-such-that-isubset-a-for-abepsilon-2/feed/ 0 70550