On some maps concerning -open sets.
On some separation axioms and -closure
On spaces whose denumerable subspaces are discrete
On strongly precontinuous functions.
On structure space of -semigroups
In this paper we introduce the notion of the structure space of -semigroups formed by the class of uniformly strongly prime ideals. We also study separation axioms and compactness property in this structure space.
On the cardinality of n-Urysohn and n-Hausdorff spaces
Two variations of Arhangelskii’s inequality for Hausdorff X [Arhangel’skii A.V., The power of bicompacta with first axiom of countability, Dokl. Akad. Nauk SSSR, 1969, 187, 967–970 (in Russian)] given in [Stavrova D.N., Separation pseudocharacter and the cardinality of topological spaces, Topology Proc., 2000, 25(Summer), 333–343] are extended to the classes with finite Urysohn number or finite Hausdorff number.
On the cardinality of Urysohn spaces and weakly -closed spaces
We introduce the cardinal invariant -, related to -, and show that if is Urysohn, then . As -, this represents an improvement of the Bella-Cammaroto inequality. We also introduce the classes of firmly Urysohn spaces, related to Urysohn spaces, strongly semiregular spaces, related to semiregular spaces, and weakly -closed spaces, related to -closed spaces.
On the extensibility of closed filters in T spaces and the existence of well orderable filter bases
We show that the statement CCFC = “the character of a maximal free filter of closed sets in a space is not countable” is equivalent to the Countable Multiple Choice Axiom CMC and, the axiom of choice AC is equivalent to the statement CFE = “closed filters in a space extend to maximal closed filters”. We also show that AC is equivalent to each of the assertions: “every closed filter in a space extends to a maximal closed filter with a well orderable filter base”, “for every set ,...
On the inverse image of Baire spaces.
On the lattice structure of topologies
On the preservation of separation axioms in products
We give sufficient and necessary conditions to be fulfilled by a filter and an ideal in order that the -quotient space of the -ideal product space preserves -properties () (“in the sense of the Łos theorem”). Tychonoff products, box products and ultraproducts appear as special cases of the general construction.
On the property p and separation axioms for bitopological spaces
On the simplicity of some categories of closure spaces
On The Sup And Inf Invariance Of Some Separation Axioms
On the sup and inf invariance of some seperation axioms.
On weak forms of preopen and preclosed functions
In this paper we introduce two classes of functions called weakly preopen and weakly preclosed functions as generalization of weak openness and weak closedness due to [26] and [27] respectively. We obtain their characterizations, their basic properties and their relationshisps with other types of functions between topological spaces.
On -generalized closed sets.
On -regular spaces.
On -closed sets and their topology.
On -resolvable and almost--resolvable spaces
We continue the study of almost--resolvable spaces beginning in A. Tamariz-Mascar’ua, H. Villegas-Rodr’ıguez, Spaces of continuous functions, box products and almost--resoluble spaces, Comment. Math. Univ. Carolin. 43 (2002), no. 4, 687–705. We prove in ZFC: (1) every crowded space with countable tightness and every space with -weight is hereditarily almost--resolvable, (2) every crowded paracompact space which is the closed preimage of a crowded Fréchet space in such a way that the...