Projectively first-countable semitopological groups
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We show that a regular semitopological group G is projectively regular first-countable if and only if G is ω-balanced, locally ω  -good and lsi1" class="mathmlsrc">lass="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166864116001450&_mathId=si1.gif&_user=111111111&_pii=S0166864116001450&_rdoc=1&_issn=01668641&md5=439b22162345b3a661b88ceb5cf60599" title="Click to view the MathML source">Ir(G)≤ωlass="mathContainer hidden">lass="mathCode">ltimg="si1.gif" overflow="scroll">lic">Irlse">(Glse">)≤ω. Similarly, we give an internal characterization of projectively lsi2" class="mathmlsrc">lass="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166864116001450&_mathId=si2.gif&_user=111111111&_pii=S0166864116001450&_rdoc=1&_issn=01668641&md5=300eb040ba2cb0c7ac32b0f4cfcc56df" title="Click to view the MathML source">Tilass="mathContainer hidden">lass="mathCode">ltimg="si2.gif" overflow="scroll">Ti first-countable semitopological groups, for lsi3" class="mathmlsrc">lass="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166864116001450&_mathId=si3.gif&_user=111111111&_pii=S0166864116001450&_rdoc=1&_issn=01668641&md5=f5f19f59da40f95dc2c624379827c211" title="Click to view the MathML source">i=0,1,2lass="mathContainer hidden">lass="mathCode">ltimg="si3.gif" overflow="scroll">i=0,1,2.

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