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We introduce and study some generalizations of regular spaces, which were motivated by studying continuity properties of functions between (regular) topological spaces. In particular, we prove that a first-countable Hausdorff topological space is regular if and only if it does not contain a topological copy of the Gutik hedgehog.
The structure of topological spaces is analysed here through the lenses of fibrous preorders. Each topological space has an associated fibrous preorder and those fibrous preorders which return a topological space are called spacial. A special class o
A Hausdorff topological group is called minimal if it does not admit a strictly coarser Hausdorff group topology. This paper mostly deals with the topological group $H_+(X)$ of order-preserving homeomorphisms of a compact linearly ordered connected s
For a non-isolated point $x$ of a topological space $X$ the network character $nw_chi(x)$ is the smallest cardinality of a family of infinite subsets of $X$ such that each neighborhood $O(x)$ of $x$ contains a set from the family. We prove that (1) e
We prove that for every $T_0$ space $X$, there is a well-filtered space $W(X)$ and a continuous mapping $eta_X: Xlra W(X)$ such that for any well-filtered space $Y$ and any continuous mapping $f: Xlra Y$ there is a unique continuous mapping $hat{f}:
Classes SSGP(n)(n < omega) of topological groups are defined, and the class-theoretic inclusions SSGP(n) subseteq SSGP(n+1) subseteq m.a.p. are established and shown proper. These classes are investigated with respect to the properties normally studi