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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
- differential topology - What does locally trivial do for us . . .
Is that correct or is there a counterexample (going either way)? The more important question is, what does locally trivial actually do for us? a There is a trivial example of fibred manifold that is not a fibre bundle if we allow our differential manifolds to be disconnected with connected components of different dimensions
- algebraic geometry - Ex. 3. 2. 2 of Qing Liu: Open immersion into locally . . .
Ex 3 2 2 of Qing Liu: Open immersion into locally Noetherian scheme is of finite type Ask Question Asked 1 year, 5 months ago Modified 1 year, 5 months ago
- Any example of a connected space that is not locally connected?
Now is there any easy enough example of a connected space that fails to be locally connected at some point? One example adduced by Munkres is the so-called topologist's sine curve, but I'm not sure why it is not locally connected
- 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 finite vs. Borel measures on $\sigma$-compact Polish spaces
I can’t think of a counter example to this, but I’m having trouble proving it My original strategy was to prove that a $\sigma$ -compact Polish space is locally compact However, as the comments demonstrate, $\sigma$ -compact Polish spaces are not necessarily locally compact, so that strategy doesn’t work
- algebraic geometry - Mathematics Stack Exchange
My attempt so far seems to sort of blow by this, and I'm not confident it's correct - if it were true, it would seem that I can completely remove the regularity condition, which seems a little drastic (I would expect that we at least need something like regular in codimension one or locally factorial)
- general topology - When is a Borel measure locally finite . . .
Question 2: Is a Borel measure on a $\sigma$ -compact space locally finite? I've asked this question before here, and a counterexample to Question 2 is proposed, but the counterexample actually doesn't work (see comments in that answer)
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