Question

Let $X$ be a topological space having only a finite number of connected components. Prove that each connected component of $X$ is open.

   Let $X$ be a topological space having only a finite number of connected components. Prove that each connected component of $X$ is open.

Mathematical physics

Mathematical physics

Robert Geroch 1st Edition

Chapter 32, Problem 223

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A connected component of a topological space \(X\) is a maximal connected subset of \(X\). This means that it is connected and cannot be properly contained in any other connected subset of \(X\). Show more…

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Let $X$ be a topological space having only a finite number of connected components. Prove that each connected component of $X$ is open.

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