Recent content by Ankit Mishra

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    Metric Space, open and closed sets

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

    (b) Show that any sub set Y of X is closed in X...is the correct question
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    Metric Space, closed ball is a closed set. prove this

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

    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...
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    Number Theory (Finite and Infinite Sets)

    Homework Statement Why is R\Q not countably infinite or denumerable? Given R (Real Number) is not countably infinite or denumerable and Q (rational number) is denumerable. Homework Equations A set is said to be denumberable or countably infinite if there exists a bijestion of N...
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    Metric Space, closed ball is a closed set. prove this

    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...