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Is there a relation between k-connectedness ( meaning 1st, 2nd,..,k-th fundamental

groups are trivial.) and having the homotopy-lifting property.? . This may be

vaguely-related to being able to extend global sections from the j-th skeleton, to

the (j+1)-st skeleton (j<=k, obviously), but I am not sure.

How about k-connectedness for a pair (A,X) ( A a subspace of X).

Thanks.

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# K-connectedness and the homotopy-lifting property

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