A local strong 𝑈𝑉^{∞}-property of the homeomorphism groups of 𝑅^{∞}- (𝑄^{∞}-) manifolds

Liem, Vo Thanh

doi:10.1090/S0002-9939-1986-0848892-9

A local strong $UV^ \infty$-property of the homeomorphism groups of $R^ \infty$- ($Q^ \infty$-) manifolds
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Proc. Amer. Math. Soc. 98 (1986), 145-149 Request permission

Abstract:

We will show in this note that if $M$ is an ${R^\infty }{\text { - (or }}{Q^\infty }{\text { - )}}$ manifold having the homotopy type of a finite complex, then the homeomorphism group of $M$, endowed with the compact-open topology, has the local strong $U{V^\infty }$-property with respect to the classes of pseudo CW complexes $\mathcal {C}\mathcal {W}(\mathcal {C})$ and $\mathcal {C}\mathcal {W}(\mathcal {M})$.

References

James Dugundji, Topology, Allyn and Bacon Series in Advanced Mathematics, Allyn and Bacon, Inc., Boston, Mass.-London-Sydney, 1978. Reprinting of the 1966 original. MR 0478089
Brayton Gray, Homotopy theory, Pure and Applied Mathematics, Vol. 64, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. An introduction to algebraic topology. MR 0402714
Vagn Lundsgaard Hansen, Some theorems on direct limits of expanding sequences of manifolds, Math. Scand. 29 (1971), 5–36. MR 319206, DOI 10.7146/math.scand.a-11031
Richard E. Heisey, Manifolds modelled on the direct limit of lines, Pacific J. Math. 102 (1982), no. 1, 47–54. MR 682043, DOI 10.2140/pjm.1982.102.47
R. E. Heisey and H. Toruńczyk, On the topology of direct limits of ANRs, Pacific J. Math. 93 (1981), no. 2, 307–312. MR 623566, DOI 10.2140/pjm.1981.93.307
J. F. P. Hudson, Piecewise linear topology, W. A. Benjamin, Inc., New York-Amsterdam, 1969. University of Chicago Lecture Notes prepared with the assistance of J. L. Shaneson and J. Lees. MR 0248844
Vo Thanh Liem, On $\textbf {R}^\infty \;(Q^\infty )$-manifold bundles over CW complexes, Trans. Amer. Math. Soc. 297 (1986), no. 2, 563–585. MR 854085, DOI 10.1090/S0002-9947-1986-0854085-6
T. Benny Rushing, Topological embeddings, Pure and Applied Mathematics, Vol. 52, Academic Press, New York-London, 1973. MR 0348752