Another property of the Sorgenfrey line
Another universal metacompact developable -space of weight m
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...
Application on local discrete expansion.
Applications of complete families of continuous functions to the theory of -spaces
Applications of limited information strategies in Menger's game
As shown by Telgársky and Scheepers, winning strategies in the Menger game characterize -compactness amongst metrizable spaces. This is improved by showing that winning Markov strategies in the Menger game characterize -compactness amongst regular spaces, and that winning strategies may be improved to winning Markov strategies in second-countable spaces. An investigation of 2-Markov strategies introduces a new topological property between -compact and Menger spaces.
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.
Applications of some strong set-theoretic axioms to locally compact T₅ and hereditarily scwH spaces
Under some very strong set-theoretic hypotheses, hereditarily normal spaces (also referred to as T₅ spaces) that are locally compact and hereditarily collectionwise Hausdorff can have a highly simplified structure. This paper gives a structure theorem (Theorem 1) that applies to all such ω₁-compact spaces and another (Theorem 4) to all such spaces of Lindelöf number ≤ ℵ₁. It also introduces an axiom (Axiom F) on crowding of functions, with consequences (Theorem 3) for the crowding of countably compact...
Approach merotopological spaces and their completion.
Approximation of with countable subsets of and calibers of the space
Approximation theorems for compactifications
We shall show several approximation theorems for the Hausdorff compactifications of metrizable spaces or locally compact Hausdorff spaces. It is shown that every compactification of the Euclidean n-space ℝⁿ is the supremum of some compactifications homeomorphic to a subspace of . Moreover, the following are equivalent for any connected locally compact Hausdorff space X: (i) X has no two-point compactifications, (ii) every compactification of X is the supremum of some compactifications whose remainder...
Approximation theoretical properties of M-ideals (Abstract)
Approximations of Stone-Cech compactifications by Higson compactifications
Archimedean and geodetical biequivalences
Are initially -compact separable regular spaces compact?
We investigate the question of the title. While it is immediate that CH yields a positive answer we discover that the situation under the negation of CH holds some surprises.
A-realcompact spaces.
Relations between homomorphisms on a real function algebra and different properties (such as being inverse-closed and closed under bounded inversion) are studied.
Around a quotient space of Bennett-Lutzer's space.
Around Katětov's metrization theorem
A-spaces and countably bi-quotient maps [Book]
Aspects of categorical algebra in initialstructure categories