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Almost-invertible spaces. (English) Zbl 0623.54011

A space is said to be semi-invertible if for each proper semi-open set U in \((X,\tau)\) there exists a semi-homeomorphism \(h: (X,\tau)\to (X,\tau)\) such that \(h(X-U)\subseteq U\). A space is said to be almost-invertible if for every non-empty regular-open subset U of (X,\(\tau)\) there exists a \(\theta\)-homeomorphism \(h:(X,\tau)\to (X,\tau)\) such that \(h(X- U)\subseteq U\). The purpose of this article is to introduce and investigate the properties of the class of almost invertible spaces which contains the class of semi-invertible spaces. A primary concern is to determine when a given local property in an almmost-invertible space is also a global property.
Reviewer: D.E.Cameron

MSC:

54C99 Maps and general types of topological spaces defined by maps
54A05 Topological spaces and generalizations (closure spaces, etc.)
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