MTH301
Question: For any vector/( X∈R^n/) the following are true, except:
Answer: /(x+y+z=2,∀x,y,z∈X/)
Question: Let X be any set and /( ∅/) be the usual empty set. If /( τ=(X,∅) /) is a topology on X, then /( τ /) is called a
Answer: indiscrete topology.
Question: The expression/( |x+y|≤ ⌈x⌉+ |y|,∀ x,y∈R/) is called
Answer: triangle inequality
Question: Let X be a vector in Then the expression /( ‖x‖=(∑_(i=1)^n▒x^(2/i) )^(1/2),∀ x∈X /) is called
Answer: the length or norm of X
Question: Let X be a nonempty set and /( Ï„ /) be the family of subsets of X., then /( Ï„ /) defines a topology on X if the following conditions are satisfied, except
Answer: /( A_(1 ) X \\A_1∈τ/)
Question: Let K be a field of scalars. Let X be a set of vectors in /( R^n,with x ∈X and αϵ K /) then we call the expression αx
Answer: a scalar multiplication
Question: Let /( x,y,z ∈R/). . Then the expression /( x+(y+z)= (x+y)+z /) , is referred to as
Answer: Associative law
Question: If R is the usual set of real numbers and /( x,y∈R with x≠y /). If x+y=y+x, we say that
Answer: R is commutative under +
Question: If there exists /( x∈R/) such that /(x.1=1.x/) then we call this 1
Answer: the multiplicative identity element of R.
Question: Let X be any set and /(Ï„={P(x)=2^x }/) be a collection of all subsets of X. If /( Ï„ /) is a topology on X, then /( (X,Ï„)/) is called
Answer: a discrete topology
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