LOCAL τ-DENSITY AND LOCAL WEAK τ-DENSITY IN TOPOLOGICAL SPACES

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.