Lebl-Basic-Analysis-I · Problem 7.2.10

Metric Spaces

Mathematics · connected-sets

Problem

Suppose {Si}\{S_i\}, i∈Ni \in \mathbb{N}, is a collection of connected subsets of a metric space (X,d)(X, d), and there exists an x∈Xx \in X such that x∈Six \in S_i for all i∈Ni \in \mathbb{N}. Show that ⋃i=1∞Si\bigcup_{i=1}^\infty S_i is connected.

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