## 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 $r \leqslant k - 3$.## References

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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