Local compactness in approach spaces. II. (English) Zbl 1106.54011

Lowen, R.; Verbeeck, C.

Int. J. Math. Math. Sci. 2003, No. 2, 109-117 (2003).

Various kinds of local compactness for approach spaces were introduced in a previous paper by the authors [Int. J. Math. Math. Sci. 21, No 3. 429–438 (1998; Zbl 0906.54020)]. In the present paper, they define an analogy of open maps for approach spaces, called expansions. It is proved that every expansive contractive image of any locally compact approach space is locally compact of the same kind. Locally compact products are characterized similarly as in topological spaces.

Reviewer: Miroslav Hušek (Praha)

MSC:

54D45	Local compactness, \(\sigma\)-compactness
54A05	Topological spaces and generalizations (closure spaces, etc.)
54B10	Product spaces in general topology

Keywords:

locally compact; approach space; open map; product