Glasnik Matematicki, Vol. 42, No.1 (2007), 83-87.

LOCAL CHARACTERIZATION OF ABSOLUTE CO-EXTENSORS

Ivan Ivanšić and Leonard R. Rubin

Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019, USA
e-mail: lrubin@ou.edu

Abstract.   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.

2000 Mathematics Subject Classification.   54C55, 54C20.

Key words and phrases.   Absolute co-extensor, absolute extensor, paracompact space, stratifiable space, local property.

DOI: 10.3336/gm.42.1.06

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