Continuous weak selections for products |
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Authors: | S. Garcí a-Ferreira,K. Miyazaki,T. Nogura |
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Affiliation: | 1. Centro de Ciencias Matemáticas, Universidad Nacional Autónoma de México, Campus Morelia, Apartado Postal 61-3, Santa María, 58089, Morelia, Michoacán, Mexico;2. Department of Mathematics, Osaka Sangyo University, Osaka 574-8530, Japan;3. Department of Mathematics, Faculty of Science, Ehime University, Matsuyama 790-8677, Japan |
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Abstract: | A weak selection on an infinite set X is a function σ:[X]2→X such that σ({x,y})∈{x,y} for each {x,y}∈[X]2. A weak selection on a space is said to be continuous if it is a continuous function with respect to the Vietoris topology on [X]2 and the topology on X . We study some topological consequences from the existence of a continuous weak selection on the product X×Y for the following particular cases:- (i)
- Both X and Y are spaces with one non-isolated point.
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Keywords: | primary, 54A10, 54C65, 54H12 secondary, 54A20, 54C05, 54F05 |
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