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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Embeddings of locally connected compacta
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by Gerard A. Venema PDF
Trans. Amer. Math. Soc. 292 (1985), 613-627 Request permission

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
  • © Copyright 1985 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 292 (1985), 613-627
  • MSC: Primary 57Q35; Secondary 54C10, 54F35, 57N15, 57N25, 57N60
  • DOI: https://doi.org/10.1090/S0002-9947-1985-0808741-5
  • MathSciNet review: 808741