A note on -operator.
A Note Related to a Paper of Noiri
A Priestley view of spatialization of frames
A research on characterizations of semi- spaces.
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.
About the first and the second constellations belonging to the topology
Abstract Characterizations of Continuous Functions.
Abstract Characterizations of Continuous Functions. (Short Communication).
Alexandroff topologies viewed as closed sets in the Cantor cube.
Algebraische Hüllenoperatoren, bei denen jede endliche Menge durch die Menge ihrer isolierten Elemente erzeugt wird
Aposyndesis in
We consider the Golomb and the Kirch topologies in the set of natural numbers. Among other results, we show that while with the Kirch topology every arithmetic progression is aposyndetic, in the Golomb topology only for those arithmetic progressions with the property that every prime number that divides also divides , it follows that being connected, being Brown, being totally Brown, and being aposyndetic are all equivalent. This characterizes the arithmetic progressions which are aposyndetic...
Applications of maximal μ-open sets in generalized topology and quasi topology
In this paper, some fundamental properties of maximal μ-open sets such as decomposition theorem for a maximal μ-open set, are given in a generalized topological space. Some basic properties of intersection of maximal μ-open sets are established, cohere the law of μ-radical μ-closure in a quasi topological space is obtained, among the other things.
Approach merotopological spaces and their completion.
Bases in -spaces
Bemerkungen zur Katastrophentheorie.
Between closed sets and generalized closed sets in closure spaces
The purpose of the present paper is to define and study -closed sets in closure spaces obtained as generalization of the usual closed sets. We introduce the concepts of -continuous and -closed maps by using -closed sets and investigate some of their properties.
Beyond Lebesgue and Baire II: Bitopology and measure-category duality
We re-examine measure-category duality by a bitopological approach, using both the Euclidean and the density topologies of the line. We give a topological result (on convergence of homeomorphisms to the identity) obtaining as a corollary results on infinitary combinatorics due to Kestelman and to Borwein and Ditor. We hence give a unified proof of the measure and category cases of the Uniform Convergence Theorem for slowly varying functions. We also extend results on very slowly varying functions...
Biframe compactifications
Compactifications of biframes are defined, and characterized internally by means of strong inclusions. The existing description of the compact, zero-dimensional coreflection of a biframe is used to characterize all zero-dimensional compactifications, and a criterion identifying them by their strong inclusions is given. In contrast to the above, two sufficient conditions and several examples show that the existence of smallest biframe compactifications differs significantly from the corresponding...
Brouwer Invariance of Domain Theorem
In this article we focus on a special case of the Brouwer invariance of domain theorem. Let us A, B be a subsets of εn, and f : A → B be a homeomorphic. We prove that, if A is closed then f transform the boundary of A to the boundary of B; and if B is closed then f transform the interior of A to the interior of B. These two cases are sufficient to prove the topological invariance of dimension, which is used to prove basic properties of the n-dimensional manifolds, and also to prove basic properties...
-biČech spaces and -biČech spaces.