Openly fatorizable spaes and ompat extensionsof topologial semi-
groups
Comment.Math.Univ.Carolin. 51,1 (2010)113{131.
Abstrat:Weprovethat thesemigroupoperationofatopologialsemigroupS extends
to aontinuoussemigroupoperation onitsStone-
Cehompatiation S providedS
is a pseudoompatopenly fatorizable spae, whihmeans that eah map f :S ! Y
to aseond ountablespae Y anbewritten asthe ompositionf =gÆp ofanopen
map p: X !Z onto aseond ountablespae Z and a map g: Z !Y. We present
aspetralharaterizationofopenlyfatorizablespaesandestablishsomepropertiesof
suhspaes.
Keywords: topologialsemigroup, semigroupompatiation,inversespetrum,pseu-
doompatspae, openly fatorizable spae, openlygenerated spae, Eberleinompat,
Corsonompat,Valdiviaompat
AMSSubjetClassiation:22A15,54B30,54C20,54C08, 54D35
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