engleski

Local characterization of absolute co-extensors

Suppose that K is a space and X is a paracompact space. We show that X is an absolute co-extensor for K (i.e., K is an absolute extensor for X) if and only if it is a local absolute co- extensor for K. We also provide a similar characterization using a weaker local extension property. The property that X is an absolute co-extensor for K is inherited by closed subsets but not necessarily by open subsets of X. We also present several extension results for open subsets of stratifiable spaces if K is a CW-complex.

Absolute co-extensor; absolute extensor; paracompact space; stratifiable space; local property

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