Basic Analysis I — Real Analysis · Problem 7.4.2

Metric Spaces — Jiri Lebl

Mathematics — Real Analysis · completeness-and-compactness

Problem

Let A:−{1/n:n∈N}⊂RA \coloneq \{1/n : n \in \mathbb{N}\} \subset \mathbb{R}. a) Show that AA is not compact directly using the definition. b) Show that A∪{0}A \cup \{0\} is compact directly using the definition.

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