arXiv subjects

A. Ravsky

Publications and source records attributed to A. Ravsky.

3 recordsLinked to original sources

arXiv2021

Embedding topological spaces into Hausdorff $κ$-bounded spaces

Let $κ$ be an infinite cardinal. A topological space $X$ is $κ$-bounded if the closure of any subset of cardinality $\leκ$ in $X$ is compact. We discuss the problem of embeddability of topological spaces into Hausdorff (Urysohn, regular) $κ$-bounded spaces, and present a canonical construction of such an embedding. Also we construct a (consistent) example of a sequentially compact separable regular space that cannot be embedded into a Hausdorff $ω$-bounded space.

math.GN↗

arXiv2015

Characterizing meager paratopological groups

We prove that a Hausdorff paratopological group G is meager if and only if there are a nowhere dense subset A of G and a countable subset C in G such that CA=G=AC.

math.GN↗

arXiv2015

Kuratowski monoids of $n$-topological spaces

Generalizing the famous 14-set closure-complement Theorem of Kuratowski from 1922, we prove that for a set $X$ endowed with $n$ pairwise comparable topologies $τ_1\subset\dots\subsetτ_n$, by repeated application of the operations of complement and closure in the topologies $τ_1,\dots,τ_n$ to a subset $A\subset X$ we can obtains at most $2K(n)=2\sum_{i,j=0}^n\binom{i+j}{i}\binom{i+j}{j}$ distinct sets.

math.GN↗