Let $X$ be a connected metric space and let $C$ be a connected subset of $X$. Let $X-C$ be a union of two separated sets $A$ and $B$. It is required to show that $C\cup A$ and $C\cup B$ are both connected. I've no idea how to approach this problem, being a beginner in this concept. Any solutions will be highly appreciated.
2026-03-30 12:27:12.1774873632
A question regarding connected subsets of connected metric spaces
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