Let R be equipped with the Euclidean topology T and let Y =]10,20[. We denote by Ty the induced topology on Y by T. Then [15,20[ is O not closed in (Y,Ty) and closed in R O closed in (Y,Ty) and closed in R O closed in (Y,Ty) and not closed in R O neither closed in (Y,Ty) nor in R

Q: Let Y be an infinite subset of a compact set X c R. Prove Y' # Ø.

A: Y' denotes the derived set of Y i.e. the set of all limit points of Y. We just need to show that any…

Q: ► Exercise 3.7. Suppose X is a topological space and UC SCX. (a) Show that the closure of U in S is…

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Q: Let X = R. Define an equivalence relation ~ on X by x ~ y if %3D and only if x – y is an integer.…

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Q: 3. If ACX such that A# 0 and r (GCX: GnA = 0}U{X} then prove that r is a topology on X. If A {p},…

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Q: Let X be an infinite set with the countable closed topology T={S subset of X; X-S is countable}.…

A: Connected means it cannot be written as union of disjoint open sets

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