On embedding of F-hedgehogs in function spaces

Abstract

For a filter F, SF = {?}?{(n,m) : n,m ? N} be the F-hedgehog (F-fan) of spininess ? where each (n,m) is isolated in SF and a basic open neighborhood of ? is of the form N(?) = {?} ?{(n,m) : n ? N,m ? ?(n)} for function ?: N ? F. We study some connections among the F*-Menger property and an embedding of F-hedgehog SF into function spaces for any P-filter F.