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Aposyndesis in ℕ

José del Carmen Alberto-Domínguez, Gerardo Acosta, Maira Madriz-Mendoza (2023)

Commentationes Mathematicae Universitatis Carolinae

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 P ( a , b ) with the property that every prime number that divides a also divides b , 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 limited information strategies in Menger's game

Steven Clontz (2017)

Commentationes Mathematicae Universitatis Carolinae

As shown by Telgársky and Scheepers, winning strategies in the Menger game characterize σ -compactness amongst metrizable spaces. This is improved by showing that winning Markov strategies in the Menger game characterize σ -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 σ -compact and Menger spaces.

Applications of maximal μ-open sets in generalized topology and quasi topology

Bishwambhar Roy, Ritu Sen (2013)

Discussiones Mathematicae - General Algebra and Applications

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

Peter J. Nyikos (2003)

Fundamenta Mathematicae

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...

Applications of the Fréchet subdifferential

Durea, M. (2003)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 46A30, 54C60, 90C26.In this paper we prove two results of nonsmooth analysis involving the Fréchet subdifferential. One of these results provides a necessary optimality condition for an optimization problem which arise naturally from a class of wide studied problems. In the second result we establish a sufficient condition for the metric regularity of a set-valued map without continuity assumptions.

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