Fuzzy extraresolvable spaces
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In this paper, a new type of resolvablity of fuzzy topological spaces, namely fuzzy extraresolvability is introduced by means of fuzzy nowhere denseness and fuzzy denseness of fuzzy sets. It is obtained that the existence of fuzzy $\sigma$-nowhere dense sets, fuzzy dense and fuzzy $G_{\delta}$-sets in fuzzy extraresolvable spaces ensures their fuzzy resolvability. It is obtained that fuzzy Baire spaces, fuzzy $DG_{\delta}$-spaces, fuzzy weakly Baire spaces become fuzzy resolvable spaces when they possesses fuzzy extraresolvability.
Abstract
In this paper, a new type of resolvablity of fuzzy topological spaces, namely fuzzy extraresolvability is introduced by means of fuzzy nowhere denseness and fuzzy denseness of fuzzy sets. It is obtained that the existence of fuzzy $\sigma$-nowhere dense sets, fuzzy dense and fuzzy $G_{\delta}$-sets in fuzzy extraresolvable spaces ensures their fuzzy resolvability. It is obtained that fuzzy Baire spaces, fuzzy $DG_{\delta}$-spaces, fuzzy weakly Baire spaces become fuzzy resolvable spaces when they possesses fuzzy extraresolvability.