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...
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| Autores principales: | , , |
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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
SpringerOpen
2009
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/65f8bacd79694b5bb987953cf162c3b3 |
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| Sumario: | 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. |
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