3 (a) Define regular, normal, completely regular, and completely normal spaces. (b) Prove that every compact Hausdorff space is regular space. (c) Prove that every subspace of a completely regular \( T_{1} \) is a completely regular \( T_{1} \).
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- A topological space is said to be normal if, given any two disjoint closed sets C and D, there exist disjoint open sets U and V such that C is in U and D is in V. - A topological space is said to be completely regular if, given any closed set C and a point x not Show more…
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