On resolvability of Lindel\"of generated spaces

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.