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Jun
7
comment Quotient manifold theorem provides a fibration?
Okay, the submersion, in fact, furnishes local sections, and therefore bundle structure. I would rather refer to the bundle structure theorem in section 7.4 of Steenrod's Topology of fiber bundles.
Jun
7
accepted Quotient manifold theorem provides a fibration?
Jun
7
revised Quotient manifold theorem provides a fibration?
added 36 characters in body
Jun
7
asked Quotient manifold theorem provides a fibration?
May
9
comment Cohomology with Coefficients in the sheaf of distributions
@ZhenLin Ugh, but why can't we restrict a Schwartz distribution to an open set? Even more, it constitutes a fine sheaf, so are sheaves of currents, which forms a fine resolution of the constant sheaf $\mathbb R$, say.
May
9
comment Why does the Residue Theorem still hold, when I let my contour get infinitely large?
You cannot make the contour infinitely large. Instead, you choose a family of contours, deriving an equation from each contour, then take limit.
May
9
comment Long exact sequence for a triple follows from long exact sequence for a pair?
Unfortunately, I had no time to check the proof, therefore I directly accepted the answer. Now it seems to me that complexes per se are more substantial than homology groups, from a viewpoint of, say, derived category or homotopical algebra. I will return this topic after pursuing homotopy theory.
May
9
accepted Long exact sequence for a triple follows from long exact sequence for a pair?
May
9
comment Comments on Eilenberg and Steenrod's “Foundations of algebraic topology” and other similar books for recomendation
And I don't know to what extent by homological algebra you mean. Just that of Cartan & Eilenberg era or of more modern stage such as derived category? Related: MO thread and this.
May
9
comment Comments on Eilenberg and Steenrod's “Foundations of algebraic topology” and other similar books for recomendation
I'm still a novice, but I think if you want an abstract, axiomatic and conceptual way towards algebraic topology, maybe homotopy-first books are more appropriate. Perhaps J.P.May's A Concise Course in Algebraic Topology works for you. It's free online.
May
9
revised The relation between homotopy equivalence and contractible mapping cone?
added 52 characters in body
May
9
asked The relation between homotopy equivalence and contractible mapping cone?
Apr
30
revised What is the motivation for the “Covering Homotopy Property” in a fibration?
edited body
Apr
22
revised Should isometries be linear?
added 1 character in body
Apr
17
comment Books on locally convex topological vector spaces
It seems to me that it's flawed that Rudin uses little categorical language, and maybe viewpoint.
Apr
17
revised Decompose a vector space into invariant subspaces?
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Apr
15
asked Decompose a vector space into invariant subspaces?
Mar
28
comment Rigorous pre-calc book with answers
@crash I didn't really understand what's pre-calculus, but I suggested Concrete Mathematics because most part of the book isn't relied on calculus and should prepare readers techniques of manipulating $\sum$, binomial coefficients, etc. Well, on the other hand, I started my first systematic study of calculus from Rudin's Principles of Mathematical Analysis. It's concise but terse and without solutions.
Mar
28
comment Does differentiability have a geometric interpretation for high dimensional functions?
It's still a linear approximation. Instead of a linear function when $m=1$, it's approximated by a linear transformation represented by the matrix.
Mar
28
comment Prove that $Ker(g \otimes k)= Im(f \otimes 1_{N}) + Im (1_{M} \otimes h)$
@LuisVera Edited. Hope it's clearer now.