Some new variants of relative regularity via regularly closed sets (Q2038572)

Summary: Every topological property can be associated with its relative version in such a way that when smaller space coincides with larger space, then this relative property coincides with the absolute one. This notion of relative topological properties was introduced by \textit{A. V. Arhangel'skii} and \textit{K. M. M. Gennedi} [``Beginnings of the theory of relative topological properties'', in: General topology. Spaces and mappings. Moscow: Lomonosov Moscow State University. 3--48 (1989)]. \textit{M. K. Singal} and \textit{S. P. Arya} introduced the concepts of almost regular spaces in [Glas. Mat., III. Ser. 4(24), 89--99 (1969; Zbl 0169.24902)] and almost completely regular spaces in [ibid. Ser. 5(25), 141--152 (1970; Zbl 0197.18901)]. In this paper, we have studied various relative versions of almost regularity, complete regularity, and almost complete regularity. We investigated some of their properties and established relationships of these spaces with each other and with the existing relative properties.