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- the equivalence of two definitions of locally closed sets
the equivalence of two definitions of locally closed sets Ask Question Asked 11 years, 8 months ago Modified 1 month ago
- Locally closed subspace - Mathematics Stack Exchange
Locally closed subspace Ask Question Asked 5 years, 3 months ago Modified 5 years, 3 months ago
- 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
- 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
- Concerning topological manifolds: Are paracompact and connected locally . . .
There are different definitions for topological manifolds, sometimes second-countability or paracompactness are added to being locally euclidian Hausdorff (Sometimes Hausdorff is also left out, bu
- Locally Closed Immersion - Mathematics Stack Exchange
But this work in exactly the opposite direction then the problem we have here Does anybody see how the auther here conclude that $\Delta_X$ is locally closed immersion?
- Any saturated subsheaf of a locally free sheaf is again locally free
I am reading Daniel Huybrechts's The Geometry of moduli spaces of sheaves In the introduction of chapter 5 He uses the following result: Proposition: Any saturated subsheaf of a locally free she
- Locally compact metric space - Mathematics Stack Exchange
So any incomplete locally compact metric space is a counter-example to "only if" Moreover, as mentioned Tsemo Aristide's answer, any non-compact metric space, even a proper one, has the same topology as some improper metric space
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