## An imbedding problem

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- by J. W. Cannon and S. G. Wayment
- Proc. Amer. Math. Soc.
**25**(1970), 566-570 - DOI: https://doi.org/10.1090/S0002-9939-1970-0259875-2
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## Abstract:

If $H$ is an uncountable collection of pairwise disjoint continua in ${E^n}$, each homeomorphic to $M$, then there exists a sequence from $H$ converging homeomorphically to an element of $H$. In the present paper the authors show that if $\{ {M_i}\}$ is a sequence of continua in ${E^n}$ which converges homeomorphically to ${M_0}$ and such that for each $i,{M_i}$ and ${M_0}$ are disjoint and equivalently imbedded, then there exists an uncountable collection $H$ of pairwise disjoint continua in ${E^n}$, each homeomorphic to $M$. For $n = 2,\;3$, and $n \geqq 5$ it is shown that one cannot guarantee that the elements of $H$ have the same imbedding as ${M_0}$.## References

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## Bibliographic Information

- © Copyright 1970 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**25**(1970), 566-570 - MSC: Primary 54.78
- DOI: https://doi.org/10.1090/S0002-9939-1970-0259875-2
- MathSciNet review: 0259875