engleski

Inverse sequences and absolute co-extensors

Suppose that K is a CW-complex, _X_ is an inverse sequence of stratifiable spaces, and X=lim(_X_). Using the concept of semi-sequence, we shall provide a necessary and sufficient condition for X to be an absolute co-extensor for K in terms of the inverse sequence _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 --> K from a closed subset A of X extends to a map F: X --> K. In case K is a polyhedron |K|_{;CW}; (the set |K| with the weak topology CW), then we will determine a similar characterization that takes into account the simplicial structure of K.

stratifiable spaces; semi-sequence; absolute (co-)extensor

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