engleski

Some applications of semi-sequences to extension theory

Suppose that K is a CW-complex, _X_ is an inverse sequence of stratifiable spaces, and X=lim(_X_). One says that X is an absolute co-extensor for K, i.e., K is an absolute extensor for X, if each map f: A --> K from a closed subset A of X extends to a map F: X --> K. This is often written X\tau K. Previously, using the concept of semi-sequence, we have provided necessary and sufficient conditions for X\tau K in terms of the inverse sequence _X_ and without recourse to any specific properties of its limit. Using such a theorem, we now prove a sufficiency result that is stronger than the ones formerly known for detecting that X\tau K. This will lead finally to a "local" version of the theorem.

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

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