The Alexandroff-Urysohn Square and the Fixed Point Property

Every continuous function of the Alexandroff-Urysohn Square into itself has a fixed point. This follows from G. S. Young's general theorem (1946) that establishes the fixed-point property for every arcwise connected Hausdorff space in which each monotone increasing sequence of arcs is contai...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	M. M. Marsh, T. H. Foregger, C. L. Hagopian
Formato:	article
Lenguaje:	EN
Publicado:	SpringerOpen 2009
Materias:	Applied mathematics. Quantitative methods T57-57.97 Analysis QA299.6-433
Acceso en línea:	https://doaj.org/article/65f8bacd79694b5bb987953cf162c3b3
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:65f8bacd79694b5bb987953cf162c3b3
record_format	dspace
spelling	oai:doaj.org-article:65f8bacd79694b5bb987953cf162c3b32021-12-02T11:31:56ZThe Alexandroff-Urysohn Square and the Fixed Point Property10.1155/2009/3108321687-18201687-1812https://doaj.org/article/65f8bacd79694b5bb987953cf162c3b32009-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2009/310832https://doaj.org/toc/1687-1820https://doaj.org/toc/1687-1812Every continuous function of the Alexandroff-Urysohn Square into itself has a fixed point. This follows from G. S. Young's general theorem (1946) that establishes the fixed-point property for every arcwise connected Hausdorff space in which each monotone increasing sequence of arcs is contained in an arc. Here we give a short proof based on the structure of the Alexandroff-Urysohn Square. M. M. MarshT. H. ForeggerC. L. HagopianSpringerOpenarticleApplied mathematics. Quantitative methodsT57-57.97AnalysisQA299.6-433ENFixed Point Theory and Applications, Vol 2009 (2009)
institution	DOAJ
collection	DOAJ
language	EN
topic	Applied mathematics. Quantitative methods T57-57.97 Analysis QA299.6-433
spellingShingle	Applied mathematics. Quantitative methods T57-57.97 Analysis QA299.6-433 M. M. Marsh T. H. Foregger C. L. Hagopian The Alexandroff-Urysohn Square and the Fixed Point Property
description	Every continuous function of the Alexandroff-Urysohn Square into itself has a fixed point. This follows from G. S. Young's general theorem (1946) that establishes the fixed-point property for every arcwise connected Hausdorff space in which each monotone increasing sequence of arcs is contained in an arc. Here we give a short proof based on the structure of the Alexandroff-Urysohn Square.
format	article
author	M. M. Marsh T. H. Foregger C. L. Hagopian
author_facet	M. M. Marsh T. H. Foregger C. L. Hagopian
author_sort	M. M. Marsh
title	The Alexandroff-Urysohn Square and the Fixed Point Property
title_short	The Alexandroff-Urysohn Square and the Fixed Point Property
title_full	The Alexandroff-Urysohn Square and the Fixed Point Property
title_fullStr	The Alexandroff-Urysohn Square and the Fixed Point Property
title_full_unstemmed	The Alexandroff-Urysohn Square and the Fixed Point Property
title_sort	alexandroff-urysohn square and the fixed point property
publisher	SpringerOpen
publishDate	2009
url	https://doaj.org/article/65f8bacd79694b5bb987953cf162c3b3
work_keys_str_mv	AT mmmarsh thealexandroffurysohnsquareandthefixedpointproperty AT thforegger thealexandroffurysohnsquareandthefixedpointproperty AT clhagopian thealexandroffurysohnsquareandthefixedpointproperty AT mmmarsh alexandroffurysohnsquareandthefixedpointproperty AT thforegger alexandroffurysohnsquareandthefixedpointproperty AT clhagopian alexandroffurysohnsquareandthefixedpointproperty
_version_	1718395822959230976

The Alexandroff-Urysohn Square and the Fixed Point Property

Ejemplares similares