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12h
comment A unique expression for a unitary complex.
How is that by definitin of $\sin$ and $\cos$?
13h
asked A unique expression for a unitary complex.
Aug
30
comment Intersection preserves homotopy equivalence
Yes i edited the question. Thanks!
Aug
30
revised Intersection preserves homotopy equivalence
edited body
Aug
30
asked Intersection preserves homotopy equivalence
Jul
25
accepted With field coefficients homology and cohomology coincide
Jul
25
comment With field coefficients homology and cohomology coincide
Ok i see what you mean now. you are saying that a finite dimensional vector space is isomorphic to its dual space. Here our vector space is $H_n(X,F)$ which when finite dimensional becomes isomorphic to its dual space $hom_F(H_n(X,F),F)$. Thank you so much!!
Jul
25
comment With field coefficients homology and cohomology coincide
Also i don't understand your sentence "and dual of a (finite dimensional ) vector space is isomorphic to itself" could you please explain what do you mean ?
Jul
25
comment With field coefficients homology and cohomology coincide
Also $H_n(X;F)$ is an $F-$ module so when you talk about finite rank, you mean finite dimension as an $F-$vector space ?
Jul
25
comment With field coefficients homology and cohomology coincide
I'm writing so to say that it is the set of $F-$module homomorphisms from the $F-$module $H_n(X;F)$ to the $F-$module $F$. This is to differentiate it from group homomorphism or any other less structure so we need homomorphisms that respect $F-$module structure. If this is what you mean buy your simpler notation by putting $F$ instead of $F-$modules ?
Jul
25
asked With field coefficients homology and cohomology coincide
Jul
25
comment Homology and Reduced homology coincide on non trivial pair.
I think you mean $C_0(A)\stackrel {\epsilon_A }{\rightarrow}\mathbb Z$ is surjective from the complex associated to $A$ and $C_0(X)\stackrel {\epsilon_X }{\rightarrow}\mathbb Z$ is surjective from the complex associated to $X$.. but $\epsilon_A$ is just the restriction homomorphism of $\epsilon_X$ hence the induced surjective homomorphism $\epsilon :C_0(X)/C_0(A)\stackrel{\epsilon}{\rightarrow} \mathbb Z$ must be zero.
Jul
25
comment Homology and Reduced homology coincide on non trivial pair.
why is the mapping $C_0(A)\stackrel {\epsilon }{\rightarrow}\mathbb Z$ surjective ? and what is $\epsilon $ here ?
Jul
25
comment Homology and Reduced homology coincide on non trivial pair.
@WillardZhan Hatcher is saying they are the same, I quoted the paragraph in my question. Could you please be more specific.. thanks!
Jul
25
asked Homology and Reduced homology coincide on non trivial pair.
Jul
21
accepted Deleting a contractible subspace is the same as deleting a point
Jul
21
comment Deleting a contractible subspace is the same as deleting a point
Yes I see thank you archipelago !!
Jul
21
comment Deleting a contractible subspace is the same as deleting a point
So you are saying there is no known result giving standard conditions on $X$ and $A$ under which removing $A$ from $X$ is the same as removing a point from $X$.
Jul
21
asked Deleting a contractible subspace is the same as deleting a point
Jul
12
awarded  Nice Question