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20h
comment Prerequisistes for P. May's A Concise Course in Algebraic Topology
Check out math.stackexchange.com/questions/716878/…
Aug
30
answered Requirement “closed under finite intersection” in Van-Kampen-Theorem
Aug
25
revised Attaching maps for the CW-decomposition of the 3-torus
added references to Blakers and Whitehead
Aug
25
answered Attaching maps for the CW-decomposition of the 3-torus
Aug
21
answered In algebraic topology, for a function $f$ what does $f _\ast$ mean?
Aug
18
comment Extension of metric definition to two sets
If you are looking for generalisations of metrics, you should consider the remarkable paper by Lawvere available at tac.mta.ca/tac/reprints/articles/1/tr1abs.html "Metric spaces, generalized logic and closed categories".
Aug
17
comment Hypothesis in homotopy equivalence inducing isomorphism in the fundamental groups
There is a generalisation of this result in 7.2.6 in my book "Topology and Groupoids".. It states that if $i:A \to X$ is a cofibration, and $f: Y \to Z$ is a homotopy equivalence, then for each map $u: A \to Y$ the induced map $f_*: [(X,i),(Y,u)] \to [(X,i),(Z,fu)]$ is a bijection. The case in the question is essentially, i,e, never mind the morphism part, when $(X,A)=(S^1,1)$.
Aug
13
revised Homology groups of the Klein bottle
added another link
Aug
11
comment Generalisation of Seifert-van Kampen theorem?
The use of more than one base point is discussed at mathoverflow.net/questions/40945/… .
Aug
7
revised Associativity of the smash product on compactly generated spaces
clarified the possibility of the counterexample to associativity
Aug
6
answered Associativity of the smash product on compactly generated spaces
Jul
28
revised Does May's version of groupoid Seifert-van Kampen need path connectivity as a hypothesis?
added a link to mathoverflow
Jul
26
comment Show $X$ is simply-connected given properties of two subsets
See also mathoverflow.net/questions/175923/…
Jul
24
comment Definition of neighborhood and open set in topology
I have added the "non empty" condition.
Jul
24
revised Definition of neighborhood and open set in topology
corrected definition and added a link
Jul
24
answered On defining homology groups
Jul
20
revised Computation of fundamental group of pseudo circle
changed "fundamental group" to the more accurate "fundamental groups"
Jul
19
revised Computation of fundamental group of pseudo circle
comment on higher homotopy groups
Jul
19
revised Computation of fundamental group of pseudo circle
added more links
Jul
18
answered Pullbacks and homotopy equivalences