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

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

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