Exercise 3.55. Show that every wedge sum of Hausdorff spaces is Hausdorff.

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Q: ( 1) Give an example of a compact space which is not Hausdorff. 2) Give an example of a locally…

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Q: cise 2 Let X be a topological space. - Show that X itself is a Baire space. T

A: Given: X is a topological space. To Prove: We have to show that the topological space X itself is a…

Q: 2) Give an example of a metric space such that the closed ball Bå(x,r) is not an open set for any x…

A: To Find: Give an example of a metric space such that a closed ball B¯d(x,r) is not open set for any…

Q: Prove that the infimum and the supremum of the interval (a,b) are a and b, respectively

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Q: Topology Let X and Y be two compact spaces, show that X×Y is compact.

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Q: snip

A: Theorem:                  Suppose <v,w> is an inner product on a vector space V.  Then…

Q: Prove or give counter example an infinite product of discrete spaces may not be discrete

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Q: Prove the following: Let (Y, d) be a metric space. If Y is totally bounded, then Y is bounded.

A: Given:  (Y,d) is a metric space, and Y is totally bounded To Prove Y is bounded Definition: Let…

Q: ( 1) Give an example of a compact space which is not Hausdorff. 2) Give an example of a locally…

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Q: Question (6): verse is not true. Contractible space simply connected space. But con-

A: A manifold X is Contactible if its identity map is homotopic to some constant map.   A manifold X…

Q: What vector space property does Q2 ={(m, n) m, n ∈ Q} fail? *set Q: rational numbers

A: Q^2 is a vector space over Q but it is not a vector space over R.