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Connectedness of some rings of quotients of C ( X ) with the m -topology

F. Azarpanah, M. Paimann, A. R. Salehi (2015)

Commentationes Mathematicae Universitatis Carolinae

In this article we define the m -topology on some rings of quotients of C ( X ) . Using this, we equip the classical ring of quotients q ( X ) of C ( X ) with the m -topology and we show that C ( X ) with the r -topology is in fact a subspace of q ( X ) with the m -topology. Characterization of the components of rings of quotients of C ( X ) is given and using this, it turns out that q ( X ) with the m -topology is connected if and only if X is a pseudocompact almost P -space, if and only if C ( X ) with r -topology is connected. We also observe that...

Connection matrix pairs

David Richeson (1999)

Banach Center Publications

We discuss the ideas of Morse decompositions and index filtrations for isolated invariant sets for both single-valued and multi-valued maps. We introduce the definition of connection matrix pairs and present the theorem of their existence. Connection matrix pair theory for multi-valued maps is used to show that connection matrix pairs obey the continuation property. We conclude by addressing applications to numerical analysis. This paper is primarily an overview of the papers [R1] and [R2].

Connections between connected topological spaces on the set of positive integers

Paulina Szczuka (2013)

Open Mathematics

In this paper we introduce a connected topology T on the set ℕ of positive integers whose base consists of all arithmetic progressions connected in Golomb’s topology. It turns out that all arithmetic progressions which are connected in the topology T form a basis for Golomb’s topology. Further we examine connectedness of arithmetic progressions in the division topology T′ on ℕ which was defined by Rizza in 1993. Immediate consequences of these studies are results concerning local connectedness of...

Connexité locale

Daniel Tanre (1974)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Consonance and Cantor set-selectors

Valentin Gutev (2013)

Open Mathematics

It is shown that every metrizable consonant space is a Cantor set-selector. Some applications are derived from this fact, also the relationship is discussed in the framework of hyperspaces and Prohorov spaces.

Constant Distortion Embeddings of Symmetric Diversities

David Bryant, Paul F. Tupper (2016)

Analysis and Geometry in Metric Spaces

Diversities are like metric spaces, except that every finite subset, instead of just every pair of points, is assigned a value. Just as there is a theory of minimal distortion embeddings of fiite metric spaces into L1, there is a similar, yet undeveloped, theory for embedding finite diversities into the diversity analogue of L1 spaces. In the metric case, it iswell known that an n-point metric space can be embedded into L1 withO(log n) distortion. For diversities, the optimal distortion is unknown....

Constant selections and minimax inequalities

Mircea Balaj (2006)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we establish two constant selection theorems for a map whose dual is upper or lower semicontinuous. As applications, matching theorems, analytic alternatives, and minimax inequalities are obtained.

Constrained optimization: A general tolerance approach

Tomáš Roubíček (1990)

Aplikace matematiky

To overcome the somewhat artificial difficulties in classical optimization theory concerning the existence and stability of minimizers, a new setting of constrained optimization problems (called problems with tolerance) is proposed using given proximity structures to define the neighbourhoods of sets. The infimum and the so-called minimizing filter are then defined by means of level sets created by these neighbourhoods, which also reflects the engineering approach to constrained optimization problems....

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