On convergence groups and convergence uniformities
On convergence groups with dense coarse subgroups
On convergence in the Mikusiński operational calculus
On Convergence of Transfinite Sequences
On convergence spaces and groups
On convergence theory in fuzzy topological spaces and its applications
In this paper we introduce and study new concepts of convergence and adherent points for fuzzy filters and fuzzy nets in the light of the -relation and the -neighborhood of fuzzy points due to Pu and Liu [28]. As applications of these concepts we give several new characterizations of the closure of fuzzy sets, fuzzy Hausdorff spaces, fuzzy continuous mappings and strong -compactness. We show that there is a relation between the convergence of fuzzy filters and the convergence of fuzzy nets similar...
On convergences of signed states
On -sequentially regular spaces
On fuzzy function spaces.
On ideal equal convergence
We consider ideal equal convergence of a sequence of functions. This is a generalization of equal convergence introduced by Császár and Laczkovich [Császár Á., Laczkovich M., Discrete and equal convergence, Studia Sci. Math. Hungar., 1975, 10(3–4), 463–472]. Our definition of ideal equal convergence encompasses two different kinds of ideal equal convergence introduced in [Das P., Dutta S., Pal S.K., On and *-equal convergence and an Egoroff-type theorem, Mat. Vesnik, 2014, 66(2), 165–177]_and [Filipów...
On idempotent filters
On local merotopic character
On mappings preserving a family of star bodies.
On meager function spaces, network character and meager convergence in topological spaces
For a non-isolated point of a topological space let be the smallest cardinality of a family of infinite subsets of such that each neighborhood of contains a set . We prove that (a) each infinite compact Hausdorff space contains a non-isolated point with ; (b) for each point with there is an injective sequence in that -converges to for some meager filter on ; (c) if a functionally Hausdorff space contains an -convergent injective sequence for some meager filter...
On metrization of hyperspaces
On monotone and pointwise splittability
On Nets and Filters.
On plane topologies with high sequential order
On quasi-p-bounded subsets
The notion of quasi-p-boundedness for p ∈ is introduced and investigated. We characterize quasi-p-pseudocompact subsets of β(ω) containing ω, and we show that the concepts of RK-compatible ultrafilter and P-point in can be defined in terms of quasi-p-pseudocompactness. For p ∈ , we prove that a subset B of a space X is quasi-p-bounded in X if and only if B × is bounded in X × , if and only if , where is the set of Rudin-Keisler predecessors of p.
On spaces with the ideal convergence property
Let I ⊆ P(ω) be an ideal. We continue our investigation of the class of spaces with the I-ideal convergence property, denoted (I). We show that if I is an analytic, non-countably generated P-ideal then (I) ⊆ s₀. If in addition I is non-pathological and not isomorphic to , then (I) spaces have measure zero. We also present a characterization of the (I) spaces using clopen covers.