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Homogeneity in powers of zero-dimensional first-countable spaces

Author(s): Alan Dow; Elliott Pearl
Journal: Proc. Amer. Math. Soc. 125 (1997), 2503-2510.
MSC (1991): Primary 54B10
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Abstract: A construction of L. Brian Lawrence is extended to show that the $\omega$ -power of every subset of the Cantor set is homogeneous via a continuous translation modulo a dense set. It follows that every zero-dimensional first-countable space has a homogeneous $\omega$ -power.

References:

1.: Gary Gruenhage, New Classic Problems: Homogeneity of $X^\infty$ , Top. Proc. 15 (1990) 207-208
2.: Gary Gruenhage and Hao-Xuan Zhou, Homogeneity of $X^\omega$ , notes
3.: O.H. Keller, Die homoiomorphie der kompakten konvexen Mengen im Hilbertschen Raum, Math. Ann. 105 (1931) 748-758 MR 41:7258
4.: L. Brian Lawrence, Homogeneity in powers of subspaces of the real line, manuscript, 1994
5.: S.V. Medvedev, Characterizations of -homogeneous metric spaces, Interim Reports of the Prague Topological Symposium 2 (1987) 19
6.: D.B. Motorov, Homogeneity and $\pi$ -networks, Moscow Univ. Math. Bull. 44 (1989) no.4, 45-50
7.: Fons van Engelen, On the homogeneity of infinite products, Top. Proc. 17 (1992) 303-315 MR 95b:54044
8.: Hao-Xuan Zhou, Homogeneity properties and power spaces, Dissertation, Wesleyan University (1993)

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Additional Information:

Alan Dow
Affiliation: Department of Mathematics and Statistics, York University, North York, Ontario, Canada M3J 1P3
Email: adow@yorku.ca

Elliott Pearl
Affiliation: Department of Mathematics and Statistics, York University, North York, Ontario, Canada M3J 1P3
Email: elliott.pearl@mathstat.yorku.ca

DOI: 10.1090/S0002-9939-97-03998-1
PII: S 0002-9939(97)03998-1
Keywords: Homogeneous, zero-dimensional, first-countable, elementary submodel
Received by editor(s): October 23, 1995
Received by editor(s) in revised form: March 4, 1996
Additional Notes: The first author acknowledges support from NSERC of Canada
Communicated by: Franklin D. Tall
Copyright of article: Copyright 1997, American Mathematical Society


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