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On a generalization of the Conley index

Marian Mrozek, James Reineck, Roman Srzednicki (1999)

Banach Center Publications

In this note we present the main ideas of the theory of the Conley index over a base space introduced in the papers [7, 8]. The theory arised as an attempt to solve two questions concerning the classical Conley index. In the definition of the index, the exit set of an isolating neighborhood is collapsed to a point. Some information is lost on this collapse. In particular, topological information about how a set sits in the phase space is lost. The first question addressed is how to retain some of...

On a generalization of uniformities

W. Kulpa (1972)

Colloquium Mathematicae

On a generalized small-object argument for the injective subcategory problem

J. Adámek, H. Herrlich, J. Rosický, W. Tholen (2002)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

On $a$ -Kasch spaces

Ali Akbar Estaji, Melvin Henriksen (2010)

Archivum Mathematicum

If $X$ is a Tychonoff space, $C (X)$ its ring of real-valued continuous functions. In this paper, we study non-essential ideals in $C (X)$ . Let $a$ be a infinite cardinal, then $X$ is called $a$ -Kasch (resp. $\bar{a}$ -Kasch) space if given any ideal (resp. $z$ -ideal) $I$ with $gen (I) < a$ then $I$ is a non-essential ideal. We show that $X$ is an $ℵ_{0}$ -Kasch space if and only if $X$ is an almost $P$ -space and $X$ is an $ℵ_{1}$ -Kasch space if and only if $X$ is a pseudocompact and almost $P$ -space. Let $C_{F} (X)$ denote the socle of $C (X)$ . For a topological space $X$ with only...

On a mechanism of choosing morphisms in concrete categories

Kučera, L., Pultr, A. (1972)

General Topology and its Relations to Modern Analysis and Algebra

On a method of constructing ANR-sets. An application of inverse limits

J. Krasinkiewicz (1976)

Fundamenta Mathematicae

On a method which leads to extremally disconnected covers

Mioduszewski, J. (1972)

General Topology and its Relations to Modern Analysis and Algebra

On a metrization of the hyperspace of a metric space

Karol Borsuk (1977)

Fundamenta Mathematicae

On a Michael's conjecture concerning the Lindelöf property in the Cartesian products

Alater, K. (1980)

Abstracta. 8th Winter School on Abstract Analysis

On a mixed-type interpolation problem for real polynomials

Zalman Rubinstein (1984)

Annales Polonici Mathematici

On a modified game of Sierpiński

Grzegorz Kubicki (1987)

Colloquium Mathematicae

On a perfect set theorem of A. H. Stone and N. N. Lusin’s constituents

J. Chaber, Gary Gruenhage, Roman Pol (1995)

Fundamenta Mathematicae

On a plane compactum with the maximal shape

S. Spież (1973)

Fundamenta Mathematicae

On a problem of Banach

W. Kulpa (1988)

Colloquium Mathematicae

On a problem of Čech

Leo Zippin (1936)

Časopis pro pěstování matematiky a fysiky

On a problem of Freudenthal's

Herbert Abels (1977)

Compositio Mathematica

On a problem of Gulevich on nonexpansive maps in uniformly convex Banach spaces

Sehie Park (1996)

Commentationes Mathematicae Universitatis Carolinae

Let $X$ be a uniformly convex Banach space, $D \subset X$ , $f : D \to X$ a nonexpansive map, and $K$ a closed bounded subset such that $\bar{co} K \subset D$ . If (1) ${f |}_{K}$ is weakly inward and $K$ is star-shaped or (2) ${f |}_{K}$ satisfies the Leray-Schauder boundary condition, then $f$ has a fixed point in $\bar{co} K$ . This is closely related to a problem of Gulevich [Gu]. Some of our main results are generalizations of theorems due to Kirk and Ray [KR] and others.

Currently displaying 81 – 100 of 1528

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Displaying 81 – 100 of 1528

On a generalization of the Conley index

On a generalization of uniformities

On a generalized small-object argument for the injective subcategory problem

On $a$ -Kasch spaces

On a mechanism of choosing morphisms in concrete categories

On a method of constructing ANR-sets. An application of inverse limits

On a method which leads to extremally disconnected covers

On a metrization of the hyperspace of a metric space

On a Michael's conjecture concerning the Lindelöf property in the Cartesian products

On a mixed-type interpolation problem for real polynomials

On a modified game of Sierpiński

On a perfect set theorem of A. H. Stone and N. N. Lusin’s constituents

On a plane compactum with the maximal shape

On a problem of Banach

On a problem of Čech

On a problem of Freudenthal's

On a problem of Gulevich on nonexpansive maps in uniformly convex Banach spaces

On a problem of H. Herrlich

On a problem of J. Nagata

On a problem of Katětov

Currently displaying 81 – 100 of 1528