On metric spaces where continuous real valued functions are uniformly continuous and related notions
Sign Up to like & getrecommendations! Published in 2018 at "Topology and its Applications"
DOI: 10.1016/j.topol.2018.02.005
Abstract: Abstract Given a metric space X = ( X , d ) we show in ZF that: (a) The following are equivalent: (i) For every two closed and disjoint subsets A , B of X,… read more here.
Keywords: real valued; continuous real; spaces continuous; uniformly continuous ... See more keywords
Ultrafilter-completeness on zero-sets of uniformly continuous functions
Sign Up to like & getrecommendations! Published in 2019 at "Topology and its Applications"
DOI: 10.1016/j.topol.2018.11.008
Abstract: Abstract The various types of ultrafilter-completeness on zero-sets of uniformly continuous functions are introduced, their properties are studied and characterizations in the category Z U n i f are given. read more here.
Keywords: continuous functions; uniformly continuous; ultrafilter completeness; sets uniformly ... See more keywords
On certain versions of straightness
Sign Up to like & getrecommendations! Published in 2020 at "Topology and its Applications"
DOI: 10.1016/j.topol.2020.107369
Abstract: Abstract Straight spaces are metric spaces X having the property that for a cover X = A ∪ B by two closed sets, any continuous function f : X → R is uniformly continuous provided… read more here.
Keywords: versions straightness; continuous functions; uniformly continuous; pre straight ... See more keywords