On resolvability of Lindel\"of generated spaces

TL;DR

This paper investigates the resolvability of Lindel"of generated spaces, establishing conditions under which such spaces are resolvable or {}-resolvable, and explores properties of L-tight spaces and their relation to dispersion character.

Contribution

It introduces new results on the resolvability of Lindel"of generated spaces and clarifies the relationship between L-tightness and resolvability in regular spaces.

Findings

Regular Lindel"of generated spaces with uncountable dispersion character are resolvable.

Hausdorff hereditarily L-spaces are L-tight spaces.

Regular L-tight spaces with uncountable dispersion character are {}-resolvable.

Abstract

In this paper we study the properties of P-generated spaces (by analogy with compactly generated). We prove that a regular Lindel\"of generated space with uncountable dispersion character is resolvable. It is proved that Hausdorff hereditarily L-spaces are L-tight spaces which were defined by Istv\'an Juh\'asz, Jan van Mill in (Variations on countable tightness, arXiv:1702.03714v1). We also prove {\omega}-resolvability of regular L-tight space with uncountable dispersion character.