文摘
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 1450&_mathId=si1.gif&_user=111111111&_pii=S0166864116001450&_rdoc=1&_issn=01668641&md5=439b22162345b3a661b88ceb5cf60599" title="Click to view the MathML source">Ir(G)≤ω. Similarly, we give an internal characterization of projectively 1450&_mathId=si2.gif&_user=111111111&_pii=S0166864116001450&_rdoc=1&_issn=01668641&md5=300eb040ba2cb0c7ac32b0f4cfcc56df" title="Click to view the MathML source">Ti first-countable semitopological groups, for 1450&_mathId=si3.gif&_user=111111111&_pii=S0166864116001450&_rdoc=1&_issn=01668641&md5=f5f19f59da40f95dc2c624379827c211" title="Click to view the MathML source">i=0,1,2.