Embeddings of Bornological Universes |
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| Authors: | Gerald Beer |
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| Affiliation: | (1) Department of Mathematics, California State University Los Angeles, 5151 State University Drive, Los Angeles, CA 90032, USA |
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| Abstract: | A bornological universe 〈X, τ, ℬ〉 is a topological space 〈X, τ〉 equipped with a bornology ℬ, that is, a cover of X that is hereditary and is closed under finite unions. In this paper, we give three different sets of necessary and sufficient conditions for the universe to be both topologically and bornologically embeddable in ℝ Y for some index set Y. When this is possible, Y can be chosen to be a family of continuous coercive functions on X. Dedicated to Arrigo Cellina. |
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| Keywords: | Bornology Embedding Coercive function One-point extension Tychonoff Embedding Theorem |
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