A note on compact-like semitopological groups
Copyright policy )A note on compact-like semitopological groups
We present a few results related to separation axioms and automatic continuity of operations in compact-like semitopological groups. In particular, is provided a semiregular semitopological group $G$ which is not $T_3$. We show that each weakly semiregular compact semitopological group is a topological group. On the other hand, constructed examples of quasiregular $T_1$ compact and $T_2$ sequentially compact quasitopological groups, which are not paratopological groups. Also we prove that a semitopological group $(G,\tau)$ is a topological group provided there exists a Hausdorff topology $\sigma\supset\tau$ on $G$ such that $(G,\sigma)$ is a precompact topological group and $(G,\tau)$ is weakly semiregular or $(G,\sigma)$ is a feebly compact paratopological group and $(G,\tau)$ is $T_3$.
напівтопологічна група, паратопологічна група, компактоподібна напівтопологічна група, компактоподібна паратопологічна група, неперервність оберненого, сукупна неперервність, аксіоми відокремлення, зліченно-компактна паратопологічна група, слабко компактн, countably compact paratopological group, compact-like semitopological group, semitopological group, paratopological group, compact-like semitopological group, compact-like paratopological group, continuity of the inverse, joint continuity, separation axioms, countably compact paratopological group, feebly compact topological group, paratopological group, compact-like paratopological group, continuity of the inverse, General Topology (math.GN), Group Theory (math.GR), 22A15, 54H99, 54H11, Connections of general topology with other structures, applications, separation axioms, QA1-939, FOS: Mathematics, Structure of topological semigroups, semitopological group, feebly compact topological group, Mathematics - Group Theory, joint continuity, Mathematics, Topological groups (topological aspects), Mathematics - General Topology
напівтопологічна група, паратопологічна група, компактоподібна напівтопологічна група, компактоподібна паратопологічна група, неперервність оберненого, сукупна неперервність, аксіоми відокремлення, зліченно-компактна паратопологічна група, слабко компактн, countably compact paratopological group, compact-like semitopological group, semitopological group, paratopological group, compact-like semitopological group, compact-like paratopological group, continuity of the inverse, joint continuity, separation axioms, countably compact paratopological group, feebly compact topological group, paratopological group, compact-like paratopological group, continuity of the inverse, General Topology (math.GN), Group Theory (math.GR), 22A15, 54H99, 54H11, Connections of general topology with other structures, applications, separation axioms, QA1-939, FOS: Mathematics, Structure of topological semigroups, semitopological group, feebly compact topological group, Mathematics - Group Theory, joint continuity, Mathematics, Topological groups (topological aspects), Mathematics - General Topology
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