Abstract
In the paper the local density and the local weak density of topological spaces are investigated. It is proved that for stratifiable spaces the local density and the local weak density coincide, these cardinal numbers are preserved under open mappings, are inverse invariant of a class of closed irreducible mappings. Moreover, it is showed that the functor of probability measures of finite supports preserves the local density of compacts.
Highlights
It is proved that for stratifiable spaces the local density and the local weak density coincide, these cardinal numbers are preserved under open mappings, are inverse invariant of a class of closed irreducible mappings
It is showed that the functor of probability measures of finite supports preserves the local density of compacts
The local properties play an important role in general topology
Summary
The local properties play an important role in general topology. For instance, compactness in Rn is equivalent to total boundedness and closedness. We say that a topological space X is locally τ -dense at a point x ∈ X if τ is the smallest cardinal number such that x has a τ -dense neighborhood in X. A topological space X is locally weakly τ dense at a point x ∈ X if τ is the smallest cardinal number such that x has a neighborhood of weak density τ in X.
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