A quasitopos containing CONV and MET as full subcategories.
A related fixed point theorem in two fuzzy metric spaces.
A Remark On Filter Regularity
A remark on filter regularity.
A remark on the Moore theorem.
A remark on the tightness of products
We observe the existence of a -compact, separable topological group and a countable topological group such that the tightness of is countable, but the tightness of is equal to .
A remark on -regular spaces.
A research on characterizations of semi- spaces.
A result forO2-convergence to be topological in posets
In this paper, the α waybelow relation, which is determined by O2-convergence, is characterized by the order on a poset, and a sufficient and necessary condition for O2-convergence to be topological is obtained.
A reverse viewpoint on the upper semicontinuity of multivalued maps
For a multivalued map between topological spaces, the upper semifinite topology on the power set is such that is upper semicontinuous if and only if it is continuous when viewed as a singlevalued map . In this paper, we seek a result like this from a reverse viewpoint, namely, given a set and a topology on , we consider a natural topology on , constructed from satisfying if , and we give necessary and sufficient conditions to the upper semicontinuity of a multivalued map ...
A set functor which commutes with all homfunctors is a homfunctor
A solution to Comfort's question on the countable compactness of powers of a topological group
In 1990, Comfort asked Question 477 in the survey book “Open Problems in Topology”: Is there, for every (not necessarily infinite) cardinal number , a topological group G such that is countably compact for all cardinals γ < α, but is not countably compact? Hart and van Mill showed in 1991 that α = 2 answers this question affirmatively under . Recently, Tomita showed that every finite cardinal answers Comfort’s question in the affirmative, also from . However, the question has remained...
A sufficient condition for maximal resolvability of topological spaces
We show a new theorem which is a sufficient condition for maximal resolvability of a topological space. We also discuss some relationships between various theorems about maximal resolvability.
A survey on topological games and their applications in analysis.
In this survey article we shall summarise some of the recent progress that has occurred in the study of topological games as well as their applications to abstract analysis. The topics given here do not necessarily represent the most important problems from the area of topological games, but rather, they represent a selection of problems that are of interest to the authors.
A topological characterization of stationary sets
A topology generated by eventually different functions
A topology with order, graph and an enumeration problem.
A tree -base for without cofinal branches
We prove an analogue to Dordal’s result in P.L. Dordal, A model in which the base-matrix tree cannot have cofinal branches, J. Symbolic Logic 52 (1980), 651–664. He obtained a model of ZFC in which there is a tree -base for with no branches yet of height . We establish that this is also possible for using a natural modification of Mathias forcing.
A Tychonoff theorem in intuitionistic fuzzy topological spaces.
A very general covering property
We introduce a general notion of covering property, of which many classical definitions are particular instances. Notions of closure under various sorts of convergence, or, more generally, under taking kinds of accumulation points, are shown to be equivalent to a covering property in the sense considered here (Corollary 3.10). Conversely, every covering property is equivalent to the existence of appropriate kinds of accumulation points for arbitrary sequences on some fixed index set (Corollary 3.5)....