Zero-selectors and GO spaces |
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Authors: | Giuliano Artico Umberto Marconi |
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Institution: | a Dipartimento di Matematica Pura e Applicata, via Belzoni 7, I-35131 Padova, Italy b Mathematical Institute of the Academy of Sciences of the Czech Republic, ?itná 25, 115 67 Prague 1, Czech Republic |
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Abstract: | We are dealing with Vietoris continuous zero-selectors, i.e., they choose for each non-empty closed set F an isolated point in F. We show that the presence of a continuous zero-selector even on a small class of non-empty closed sets of a space X implies that X is scattered if X is metrizable or non-Archimedean or a P-space. Finally, using continuous zero-selectors, we characterize suborderable spaces which are subspaces of ordinals. |
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Keywords: | 54C65 54B20 54F05 54G12 |
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