#### 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 Zagreb,
Unska 3, P.O. Box 148, 10001 Zagreb, Croatia

*e-mail:* `ivan.ivansic@fer.hr`
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.

**Full text (PDF)** (free access)
DOI: 10.3336/gm.42.1.06

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