This article is cited in 2 papers

Geometry and topology

Local $\tau$-density and local weak $\tau$-density in topological spaces

T. K. Yuldashev, F. G. Mukhamadiev

National University of Uzbekistan, 4, Universitetskaya str., 100174, Tashkent, Uzbekistan

Abstract: The article considers locally compact, metrizable, and linearly ordered spaces. In these spaces, the concepts of local $\tau$-density and local weak $\tau$-density are considered. It is shown that in locally compact, metrizable, and linearly ordered spaces the concepts of local $\tau$-density and local weak $\tau$-density coincide. It is proved that a locally weakly $\tau$-dense subset of a compact set with the first axiom of countability is locally $\tau$-dense.

Keywords: local $\tau$-density, local weak $\tau$-density, locally compact space, metrizable space, linearly ordered space.

UDC: 515.1

MSC: 54B20, 54A25

Received June 24, 2020, published April 28, 2021

Language: English

DOI: 10.33048/semi.2021.18.033

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