A good pair $(A,X)$ is such that $A\subset X$ and there is a neighborhood deformation retract of A in X. What are some examples of bad pairs? I think $(A,I)$ where $A = ${$0,1,1/2,1/3...$} is a bad pair (is it?). Are there any other examples?
2026-02-23 10:22:31.1771842151
What are some examples of bad pairs $(A,X)$?
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Every time when $X$ is locally connected, but $A$ is not, it will be a bad pair. This covers your example and many many more, e.g. Cantor set in $\mathbb{R}$, comb space in $\mathbb{R}^2$, etc.