M. A. Filatova, A. V. Osipov, “On resolvability of Lindelöf generated spaces”, Sib. Èlektron. Mat. Izv., 2018, Volume 15,Pages <nobr>1260

This article is cited in 1 paper

Geometry and topology

On resolvability of Lindelöf generated spaces

M. A. Filatova^ab, A. V. Osipov^acb

^a Krasovskii Institute of Mathematics and Mechanics, 16 S.Kovalevskaya str. 620990, Yekaterinburg, Russia
^b Ural Federal University, 19 Mira str., 620002, Yekaterinburg, Russia
^c Ural State University of Economics, 62, 8th of March str., 620219, Yekaterinburg, Russia

Abstract: In this paper we study the properties of $\mathscr{P}$ 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 $\omega$-resolvability of regular $L$-tight space with uncountable dispersion character.

Keywords: resolvable space, $k$-space, tightness, $\omega$-resolvable space, Lindelöf generated space, $\mathscr{P}$ generated space, $\mathscr{P}$-tightness.

UDC: 515.1

MSC: 54A25

Received November 29, 2017, published October 23, 2018

Language: English

DOI: 10.17377/semi.2018.15.102