Long, Paul E.; Herrington, Larry L.; Janković, Dragan S. Almost-invertible spaces. (English) Zbl 0623.54011 Bull. Korean Math. Soc. 23, 91-102 (1986). 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 Cited in 1 Document MSC: 54C99 Maps and general types of topological spaces defined by maps 54A05 Topological spaces and generalizations (closure spaces, etc.) Keywords:semi-open set; regular-open subset; almost invertible spaces; semi- invertible spaces PDFBibTeX XMLCite \textit{P. E. Long} et al., Bull. Korean Math. Soc. 23, 91--102 (1986; Zbl 0623.54011)