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awarded  Nice Answer
Apr
27
comment Local “pathologies” in spaces arising naturally in algebraic topology
Jon, I and many others work with more general spaces. If one is interested in parametrized homotopy theory or using the classifying spaces BAut(X) for infinite CW complexes X, for example, one is immediately outside such unnatural restrictions, even outside spaces of the homotopy type of CW complexes (which of course is far more natural than CW complexes). Even a purely stable homotopy theorist might consider spaces such as QX.
Apr
25
comment Local “pathologies” in spaces arising naturally in algebraic topology
Denis, what never? Consistency is the hobgoblin ...
Apr
25
comment “structure group” for fibration
Mike, thanks for the reference. For others, his comment about larger X is that there is no need to restrict to finite CW complexes. That ensures that Aut(X) has the homotopy type of a CW complex, but the proofs in ``Classifying spaces and fibrations'' don't require that. Denis, if memory serves, I think that Milnor was the first to see that you can replace M by a topological group.
Apr
25
awarded  Nice Answer
Apr
16
comment Generalization of the fiber changing trick for principal bundles?
One would do well to go back to Norman Steenrod's classical book "The topology of fiber bundles'', where it is made clear how to construct bundles of either sort in terms of coordinate transformations defined solely in terms of the base space and the group G. No cellular structure needed. See Theorem 3.3, page 16.
Apr
16
comment Structure theorem for infinitely generated modules over a PID
Another excellent book on the subject is Irving Kaplinsky. Infinite abelian groups. University of Michigan Press, Ann Arbor, 1954.
Apr
15
comment Where does Segal's category come from?
Another remark about that functor. We may view it as a contravariant functor landing in the (skeletal) category of finite based sets. It is then nothing but the standard simplicial circle S^1 = \Delta[1]/\partial \Delta[1].
Apr
14
comment Topological localization of (infinite) inverse limits
Localization (of abelian groups) does not commute with infinite products. Since localization (of simple spaces) localizes homotopy groups, I think one cannot expect a simple general answer. The question has to be first answered on the group level.
Apr
5
answered $RO(G)$-graded homotopy groups vs. Mackey functors
Apr
3
awarded  Nice Answer
Mar
20
answered Massey products in the Steenrod algebra
Mar
14
comment How to stop worrying about enriched categories?
On the contrary, that is the standard defn of 2-categories, from way back.
Mar
11
comment The properness of the special singular simplicial spaces
On second thought, I am not so sure about the claim that S takes values in proper simplicial based spaces. The author seems to have been careless.
Mar
10
answered Path space of a simplicial topological space?
Mar
10
answered The properness of the special singular simplicial spaces
Feb
5
awarded  Nice Answer
Feb
5
revised Intuition/idea behind a proof of the splitting principle?
added 5 characters in body
Feb
5
answered Intuition/idea behind a proof of the splitting principle?
Feb
4
awarded  Nice Answer