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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Embeddings of locally connected compacta


Author: Gerard A. Venema
Journal: Trans. Amer. Math. Soc. 292 (1985), 613-627
MSC: Primary 57Q35; Secondary 54C10, 54F35, 57N15, 57N25, 57N60
MathSciNet review: 808741
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Abstract: Let $ X$ be a $ k$-dimensional compactum and $ f:X \to {M^n}$ a map into a piecewise linear $ n$-manifold, $ n \geqslant k + 3$. The main result of this paper asserts that if $ X$ is locally $ (2k - n)$-connected and $ f$ is $ (2k - n + 1)$-connected, then $ f$ is homotopic to a CE equivalence. In particular, every $ k$-dimensional, $ r$-connected, locally $ r$-connected compactum is CE equivalent to a compact subset of $ {{\mathbf{R}}^{2k - r}}$ as long as $ r \leqslant k - 3$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0808741-5
PII: S 0002-9947(1985)0808741-5
Keywords: Cell-like set, compactum, CE map, CE equivalence, topological embedding, $ r$-connected, locally $ r$-connected
Article copyright: © Copyright 1985 American Mathematical Society