2019/07/25 by Ravsky, Alex
#22A15 #54H11 #54H99 #FOS: Mathematics #General Topology (math.GN) #Group Theory (math.GR)
paper · doi:10.48550/arxiv.1907.11215
The note contains a few results related to separation axioms and automatic continuity of operations in compact-like semitopological groups. In particular, is presented a semiregular semitopological group G which is not T3. We show that each weakly semiregular compact semitopological group is a topological group. On the other hand, constructed examples of quasiregular T1 compact and T2 sequentially compact quasitopological groups, which are not paratopological groups. Also we prove that a semitopological group (G,τ) is a topological group provided there exists a Hausdorff topology σ⊃τ on G such that (G,σ) is a precompact topological group and (G,τ) is weakly semiregular or (G,σ) is a feebly compact paratopological group and (G,τ) is T3.