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35m
awarded  Constituent
7h
comment How do I prove that a finite covering space of a compact space is compact?
More generally a finite covering space is proper : see here
7h
comment How do I prove that a finite covering space of a compact space is compact?
More generally a finite covering space is proper : see here
12h
comment Covering map is proper $\iff$ it is finite-sheeted
You are welcome. On the other hand it was easier for me to write on a screen than for you on a banana...
12h
answered Covering map is proper $\iff$ it is finite-sheeted
12h
comment Singular Points on Algebraic Curves
@Robert This would be hard to generalize to all commutative rings with unity Really? Just ask a question about that and we'll see...
13h
answered Singular Points on Algebraic Curves
1d
comment Cohomology of affine plane with double origin
Caro Giulio, I took the liberty of correcting a typo in the fourth line. I also upvoted your magnificent answer and I encourage others to do so too. Could you perhaps, if you feel so inclined and have the time , explicitate some of the maps and add a reference for Mayer-Vietoris ?
1d
revised Cohomology of affine plane with double origin
added 14 characters in body
2d
answered How do I prove that a finite covering space of a compact space is compact?
2d
comment Is every open set in a base space evenly covered?
@Daniel: I think we agree .
2d
comment Is every open set in a base space evenly covered?
@Daniel: I disagree with your objection. Your covering is not the product $B\times D$ of the base with a discrete space. In my second description it is obvious that I mean that the disjoint union is mapped to the base by a mapping that restricts to the identity on each summand, and not to some artificially constructed map. By the way, considerations of connected components are irrelevant in my definition, which is general and valid for a completely disconnected base for example.
2d
comment Is every open set in a base space evenly covered?
The covering $C\to B$ is trivial if it is a product $C=B \times D$ with $D$ a discrete space. Equivalently, $C$ is a disjoint sum of copies of $B$.
2d
awarded  Nice Answer
2d
answered Is every open set in a base space evenly covered?
2d
revised “Advice to young mathematicians”
added 403 characters in body
2d
comment Basic question related to sheaf of a scheme
The open subset $U\subset X$ is a scheme in its own right so you may and should forget about $U$ and just ask whether $\Gamma(X,\mathcal O_X)\neq 0$ for a non-empty scheme $X$ ! And the answer is then obviously yes by considering any non-empty open affine $V=Spec(A)\subset X$ and the restriction ring morphism $\Gamma(X,\mathcal O_X)\to \Gamma(V,\mathcal O_X)=A$.
2d
answered parallelizable manifolds
2d
revised Does there exist a regular map $\mathbb{A}^1\to\mathbb{P}^1$ which is surjective?
suppressed a meaningless "t" in "By algebra"
Dec
16
comment Does there exist a regular map $\mathbb{A}^1\to\mathbb{P}^1$ which is surjective?
Very nice, because down-to-earth, question!