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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 studied by topologists (products, quotients, passage to dense subgroups, and the like). In passing the authors establish the presence of the SSGP(1) or SSGP(2) property in many of the early examples in the literature of abelian m.a.p. groups.
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
Known and new results on free Boolean topological groups are collected. An account of properties which these groups share with free or free Abelian topological groups and properties specific of free Boolean groups is given. Special emphasis is placed
A topological group $G$ is called an $M_omega$-group if it admits a countable cover $K$ by closed metrizable subspaces of $G$ such that a subset $U$ of $G$ is open in $G$ if and only if $Ucap K$ is open in $K$ for every $KinK$. It is shown that any t
It is proved that any countable topological group in which the filter of neighborhoods of the identity element is not rapid contains a discrete set with precisely one nonisolated point. This gives a negative answer to Protasovs question on the existe
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 reg