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: Posted on:
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 ____________________________ Posted on:
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 Posted on:
Let X be a set. A topology on X is acollection \(\tau \)of subsets of X, for which one of these does not hold: Posted on:
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 = Posted on:
