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Prove that no subset of a Hausdorff topological space, with the subset consisting of exactly two points, can be connected. Figure 93 can't copy

   Prove that no subset of a Hausdorff topological space, with the subset consisting of exactly two points, can be connected.
Figure 93 can't copy

Mathematical physics

Mathematical physics

Robert Geroch 1st Edition

Chapter 32, Problem 218

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Step 1

A topological space is connected if it cannot be divided into two disjoint non-empty open sets. In other words, there do not exist two open sets \( U \) and \( V \) such that the space is the union of \( U \) and \( V \), and both \( U \cap V = \emptyset \) and \( Show more…

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Prove that no subset of a Hausdorff topological space, with the subset consisting of exactly two points, can be connected. Figure 93 can't copy

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