On resolvability of Lindelöf generated spaces

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In this paper we study the properties of P-generated spaces (by analogy with compactly generated). We prove that a regular Lindelöf generated space with uncountable dispersion character is resolvable. It is proved that Hausdorff hereditarily L-spaces are L-tight spaces which were defined by István Juhász, Jan van Mill in (Variations on countable tightness, arXiv:1702.03714v1). We also prove ω-resolvability of regular L-tight space with uncountable dispersion character.