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...
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | article |
| Langue: | EN |
| Publié: |
SpringerOpen
2009
|
| Sujets: | |
| Accès en ligne: | https://doaj.org/article/65f8bacd79694b5bb987953cf162c3b3 |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| Résumé: | 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. |
|---|