- general topology - Is every compact space locally compact . . .
4 This is true trivially A space is locally compact if every point has a compact neighborhood If the space itself is compact, then it is a compact neighborhood of every point
- Compactness, Local Compactness, Completeness - Mathematics Stack Exchange
Clearly, every compact metric space is locally compact I always get confused when completeness is introduced into the picture Which of the following are true? What are some easy counterexamples to
- quotients of locally compact space - Mathematics Stack Exchange
The closed continuous image of a locally compact space is locally compact, provided the pre-image of each point is compact Maybe the question is very obvious but I can't see where to start a demonstration, Any suggestion or contribution is welcome, thanks!
- Local-global properties (localization): free, projective, injective . . .
Please define "torsion-free" and "divisible" Do you think "free" is local-global ?
- Is connectedness $\implies - Mathematics Stack Exchange
Neither connected nor locally connected implies the other, nor do their negations Four examples: $\Bbb R$ is connected and locally connected $ [1,2] \cup [3,4]$ is locally connected but not connected The topologist's sine curve is connected but not locally connected $\Bbb Q$ is neither
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