## Homeomorphism groups of some direct limit spaces

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- by Margie Hale PDF
- Proc. Amer. Math. Soc.
**85**(1982), 661-665 Request permission

## Abstract:

Let $F$ be either of the spaces ${R^\infty } = {R^n}$ or ${Q^\infty } = {Q^n}$ where $R$ denotes the reals and $Q$ the Hilbert cube. Let $\mathcal {H}(M)$ be the homeomorphism group of a connected $F$-manifold $M$ with the compact-open topology. We prove that $\mathcal {H}(M)$ is separable, LindelΓΆf, paracompact, non-first-countable, and not a $k$-space.## References

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## Additional Information

- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**85**(1982), 661-665 - MSC: Primary 57S05; Secondary 54H15, 57N20, 58B05
- DOI: https://doi.org/10.1090/S0002-9939-1982-0660625-4
- MathSciNet review: 660625