The subcontinua of a dendron form a Hilbert cube factor
HTML articles powered by AMS MathViewer
- by James E. West
- Proc. Amer. Math. Soc. 36 (1972), 603-608
- DOI: https://doi.org/10.1090/S0002-9939-1972-0312449-9
- PDF | Request permission
Abstract:
The title statement is proved, and it is shown further that the subcontinua of a dendron actually form a Hilbert cube when (and only when) the branch points of the dendron are dense. Along the way, it is established that whenever a Hilbert cube manifold is compactified into a Hilbert cube factor by the addition of another Hilbert cube factor having Property Z in the compactification, then the resulting space is actually a Hilbert cube.References
- R. D. Anderson, The Hilbert cube as a product of dendrons, Notices Amer. Math. Soc. 11 (1964), 572. Abstract #614-649.
- R. D. Anderson, On topological infinite deficiency, Michigan Math. J. 14 (1967), 365β383. MR 214041
- R. D. Anderson and R. Schori, Factors of infinite-dimensional manifolds, Trans. Amer. Math. Soc. 142 (1969), 315β330. MR 246327, DOI 10.1090/S0002-9947-1969-0246327-5
- R. D. Anderson, David W. Henderson, and James E. West, Negligible subsets of infinite-dimensional manifolds, Compositio Math. 21 (1969), 143β150. MR 246326
- Morton Brown, Some applications of an approximation theorem for inverse limits, Proc. Amer. Math. Soc. 11 (1960), 478β483. MR 115157, DOI 10.1090/S0002-9939-1960-0115157-4
- R. Duda, On the hyperspace of subcontinua of a finite graph. I, Fund. Math. 62 (1968), 265β286. MR 236881, DOI 10.4064/fm-62-3-265-286
- R. Duda, On the hyperspace of subcontinua of a finite graph. I, Fund. Math. 62 (1968), 265β286. MR 236881, DOI 10.4064/fm-62-3-265-286
- R. Duda, Correction to the paper: βOn the hyperspace of subcontinua of a finite graph. Iβ, Fund. Math. 69 (1970), 207β211. MR 273575, DOI 10.4064/fm-69-3-207-211
- James Eells Jr. and Nicolaas H. Kuiper, Homotopy negligible subsets, Compositio Math. 21 (1969), 155β161. MR 253331
- Ott-Heinrich Keller, Die Homoiomorphie der kompakten konvexen Mengen im Hilbertschen Raum, Math. Ann. 105 (1931), no.Β 1, 748β758 (German). MR 1512740, DOI 10.1007/BF01455844
- R. Schori and J. E. West, $2^{I}$ is homeomorphic to the Hilbert cube, Bull. Amer. Math. Soc. 78 (1972), 402β406. MR 309119, DOI 10.1090/S0002-9904-1972-12917-3 β, The hyperspace of the unit interval (to appear). β, Hyperspaces of finite graphs (to appear).
- James E. West, Infinite products which are Hilbert cubes, Trans. Amer. Math. Soc. 150 (1970), 1β25. MR 266147, DOI 10.1090/S0002-9947-1970-0266147-3
- James E. West, Mapping cylinders of Hilbert cube factors, General Topology and Appl. 1 (1971), no.Β 2, 111β125. MR 288788
- Gordon Thomas Whyburn, Analytic Topology, American Mathematical Society Colloquium Publications, Vol. 28, American Mathematical Society, New York, 1942. MR 0007095
Bibliographic Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 36 (1972), 603-608
- MSC: Primary 54B20; Secondary 54A20
- DOI: https://doi.org/10.1090/S0002-9939-1972-0312449-9
- MathSciNet review: 0312449