The 2-topology, Whyburn Type Filters and the Cluster Set Map
نویسندگان
چکیده
We use nonstandard topology and the g-topology to characterize normal, almost-normal, regular, almost-regular, semiregular spaces. The cluster [resp. 0-cluster] set relation is used to characterize regular, almostregular [resp. strongly-regular] spaces. The Whyburn [resp. Dickman] filter bases are characterized and it is shown that the cluster [resp. f-cluster] set relation restricted to the domain of the Whyburn [resp. Dickman] filter bases is an essentially continuous [resp. strongly 0-continuous] map iff the space is Hausdorff [resp. Urysohn].
منابع مشابه
A kind of fuzzy upper topology on L-preordered sets
Considering a commutative unital quantale L as the truth value table and using the tool of L-generalized convergence structures of stratified L-filters, this paper introduces a kind of fuzzy upper topology, called fuzzy S-upper topology, on L-preordered sets. It is shown that every fuzzy join-preserving L-subset is open in this topology. When L is a complete Heyting algebra, for every completel...
متن کاملInverse topology in BL-algebras
In this paper, we introduce Inverse topology in a BL-algebra A and prove the set of all minimal prime filters of A, namely Min(A) with the Inverse topology is a compact space, Hausdorff, T0 and T1-Space. Then, we show that Zariski topology on Min(A) is finer than the Inverse topology on Min(A). Then, we investigate what conditions may result in the equivalence of these two topologies. Finally,...
متن کاملZero elements and $z$-ideals in modified pointfree topology
In this paper, we define and study the notion of zero elements in topoframes; a topoframe is a pair $(L, tau)$, abbreviated $L_{ tau}$, consisting of a frame $L$ and a subframe $ tau $ all of whose elements are complemented elements in $L$. We show that the $f$-ring $ mathcal{R}(L_tau)$, the set of $tau$-real continuous functions on $L$, is uniformly complete. Also, t...
متن کاملSTABILIZER TOPOLOGY OF HOOPS
In this paper, we introduce the concepts of right, left and product stabilizers on hoops and study some properties and the relation between them. And we try to find that how they can be equal and investigate that under what condition they can be filter, implicative filter, fantastic and positive implicative filter. Also, we prove that right and product stabilizers are filters and if they are ...
متن کاملZero sets in pointfree topology and strongly $z$-ideals
In this paper a particular case of z-ideals, called strongly z-ideal, is defined by introducing zero sets in pointfree topology. We study strongly z-ideals, their relation with z-ideals and the role of spatiality in this relation. For strongly z-ideals, we analyze prime ideals using the concept of zero sets. Moreover, it is proven that the intersection of all zero sets of a prime ideal of C(L),...
متن کامل