On Almost Moscow Topological Groups

This paper introduces almost Moscow topological groups, a novel class of topological algebraic structures that unifies the almost continuity with the Gδ-regularity. The study establishes that every almost Moscow space is δ-extremally disconnected, with strict converse failure. The framework yields sharp characterizations such as an almost Moscow topological group is extremally disconnected iff locally countably S-closed and km-perfect, further a locally rc-Lindelöf mildly Hausdorff induces δ-extremally disconnected. Additionally, semi-regularizations of locally countably rc-paracompact groups are ω-extremally disconnected. Consequently, Hausdorff semi-regular first countable locally countably rc-paracompact members are discrete. In the extremally disconnected setting, every such group contains an open Boolean subgroup. Moreover, locallycountably S-closed km-perfect almost Moscow topological groups are extremally disconnected topological groups that are strong PT-groups. Results on δ-closures, rc-Lindelöf equivalences, and homomorphic permanence establish a robust foundation for algebraic operations under weakened continuity, with applications to completion theory, quotient structures, and generalized topological dynamics.