All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 6 Next

Displaying 101 – 120 of 123

Showing per page

Stable cohomotopy groups of compact spaces

Sławomir Nowak (2003)

Fundamenta Mathematicae

We show that one can reduce the study of global (in particular cohomological) properties of a compact Hausdorff space X to the study of its stable cohomotopy groups π s k ( X ) . Any cohomology functor on the homotopy category of compact spaces factorizes via the stable shape category ShStab. This is the main reason why the language and technique of stable shape theory can be used to describe and analyze the global structure of compact spaces. For a given Hausdorff compact space X, there exists a metric compact...

Strong shape of the Stone-Čech compactification

Sibe Mardešić (1992)

Commentationes Mathematicae Universitatis Carolinae

J. Keesling has shown that for connected spaces X the natural inclusion e : X → β X of X in its Stone-Čech compactification is a shape equivalence if and only if X is pseudocompact. This paper establishes the analogous result for strong shape. Moreover, pseudocompact spaces are characterized as spaces which admit compact resolutions, which improves a result of I. Lončar.

The homotopies of admissible multivalued mappings

Mirosław Ślosarski (2012)

Open Mathematics

Certain properties of homotopies of admissible multivalued mappings shall be presented, along with their applications as the tool for examining the acyclicity of a space.

The Vietoris system in strong shape and strong homology

Bernd Günther (1992)

Fundamenta Mathematicae

We show that the Vietoris system of a space is isomorphic to a strong expansion of that space in the Steenrod homotopy category, and from this we derive a simple description of strong homology. It is proved that in ZFC strong homology does not have compact supports, and that enforcing compact supports by taking limits leads to a homology functor that does not factor over the strong shape category. For compact Hausdorff spaces strong homology is proved to be isomorphic to Massey's homology.

Topology and dynamics of unstable attractors

M. A. Morón, J. J. Sánchez-Gabites, J. M. R. Sanjurjo (2007)

Fundamenta Mathematicae

This article aims to explore the theory of unstable attractors with topological tools. A short topological analysis of the isolating blocks for unstable attractors with no external explosions leads quickly to sharp results about their shapes and some hints on how Conley's index is related to stability. Then the setting is specialized to the case of flows in ℝⁿ, where unstable attractors are seen to be dynamically complex since they must have external explosions.

Uniformly Movable Categories and Uniform Movability of Topological Spaces

P. S. Gevorgyan, I. Pop (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

A categorical generalization of the notion of movability from inverse systems and shape theory was given by the first author who defined the notion of movable category and used it to interpret the movability of topological spaces. In this paper the authors define the notion of uniformly movable category and prove that a topological space is uniformly movable in the sense of shape theory if and only if its comma category in the homotopy category HTop over the subcategory HPol of polyhedra is uniformly...

Variations on a theme of homotopy

Timothy Porter (2013)

Annales de la faculté des sciences de Toulouse Mathématiques

The aim of this article is to bring together various themes from fairly elementary homotopy theory and to examine them, in part, from a historical and philosophical viewpoint.

Currently displaying 101 – 120 of 123