ON FINITE-DIMENSIONAL MAPS
Let f: X → Y be a perfect surjective map of paracompact spaces. It is shown that if Y is a C-space (resp., dim Y ≤ n and dim f ≤ m), then the function space C(X, I∞) (resp., C(X, I2n+1+ m)) equipped with the source limitation topology contains a dense Gδ-set K such that f × g embeds X into Y × I∞(re...
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| Veröffentlicht in: | Tsukuba journal of mathematics 2004-06, Vol.28 (1), p.155-167 |
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| container_title | Tsukuba journal of mathematics |
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| creator | Tuncali, H. Murat Valov, Vesko |
| description | Let f: X → Y be a perfect surjective map of paracompact spaces. It is shown that if Y is a C-space (resp., dim Y ≤ n and dim f ≤ m), then the function space C(X, I∞) (resp., C(X, I2n+1+ m)) equipped with the source limitation topology contains a dense Gδ-set K such that f × g embeds X into Y × I∞(resp., into Y × I2n+1+m) for every g ∊ K. Some applications of this result are also given. |
| doi_str_mv | 10.21099/tkbjm/1496164719 |
| format | Article |
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| ispartof | Tsukuba journal of mathematics, 2004-06, Vol.28 (1), p.155-167 |
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| language | eng |
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| source | JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing; Open Access Titles of Japan; Alma/SFX Local Collection |
| subjects | Embeddings Function spaces Hurewicz theorem Mathematical theorems Metric spaces Topological dimensions Topological spaces Topological theorems Topology |
| title | ON FINITE-DIMENSIONAL MAPS |
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