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2 questions
4
votes
1
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Metric space that can be written as the finite union of connected subsets but isn't locally connected
I'm looking for an example of a metric space $X$ such that for every $\epsilon > 0$ there exist connected subsets $A_1, \dots A_n$ for some $n \in \mathbb{N}$ such that $X = \cup_{i = 1}^nA_i$ and ...
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2
votes
1
answer
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Boundaries in Spaces where Quasicomponents and Components Coincide
Let's call a space $X$ geometric if its components and quasi-components coincide. Let's also define a property called the boundary bumping property:
$X$ has the boundary bumping property ("bbp&...
- 393