Inverse Sequences and Absolute Co-Extensors
Volume 55 / 2007
Bulletin Polish Acad. Sci. Math. 55 (2007), 243-259
MSC: 54C55, 54B35, 54F45.
DOI: 10.4064/ba55-3-6
Abstract
Suppose that is a CW-complex, \mathbf{X} is an inverse sequence of stratifiable spaces, and X=\lim\mathbf{X}. Using the concept of semi-sequence, we provide a necessary and sufficient condition for X to be an absolute co-extensor for K in terms of the inverse sequence \mathbf{X} and without recourse to any specific properties of its limit. To say that X is an absolute co-extensor for K is the same as saying that K is an absolute extensor for X, i.e., that each map f:A\to K from a closed subset A of X extends to a map F:X\to K. In case K is a polyhedron |K|_{\rm CW} (the set |K| with the weak topology \rm CW), we determine a similar characterization that takes into account the simplicial structure of K.
