Basic Analysis I — Real Analysis · Problem 7.2.11

Metric Spaces — Jiri Lebl

Mathematics — Real Analysis · open-and-closed-sets

Problem

Let AA be a connected set in a metric space. a) Is A‾\overline{A} connected? Prove or find a counterexample. b) Is A∘A^\circ connected? Prove or find a counterexample. Hint: Think of sets in R2\mathbb{R}^2.

Related theory

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