Recent content by Ankit Mishra

the set {y | d(x,y) < 1/2}...how was developed? and why less than 1/2?

(b) Show that any sub set Y of X is closed in X...is the correct question

Well I wrote that the boundary points in a closed ball are contained, but i don't know how to prove it?

Homework Statement Let X be set donoted by the discrete metrics d(x; y) =(0 if x = y; 1 if x not equal y: (a) Show that any sub set Y of X is open in X (b) Show that any sub set Y of X is closed in y Homework Equations In a topological space, a set is closed if and only if it...

Homework Statement Why is R\Q not countably infinate or denumerable? Given R (Real Number) is not countably infinate or denumerable and Q (rational number) is denumerable. Homework Equations A set is said to be denumberable or countably infinate if there exists a bijestion of N...

Homework Statement Let (X, d) be a metric space. The set Y in X , d(x; y) less than equal to r is called a closed set with radius r centred at point X. Show that a closed ball is a closed set. Homework Equations In a topological space, a set is closed if and only if it coincides...