A note on compact-like semitopological groups - Ravsky, A. (Carpathian Mathematical Publications, 2019)
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,τ) is a topological group provided there exists a Hausdorff topology στ 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 T_3.