Proceedings of the American Mathematical Society

Author(s): A. V. Ostrovsky
Journal: Proc. Amer. Math. Soc. 128 (2000), 3081-3089.
MSC (1991): Primary 54C10, 54D18
Posted: March 2, 2000
Retrieve article in: PDF
This article is available free of charge

Abstract: We define the notions of stable and transquotient maps and study the relation between these classes of maps. The class of stable maps contains all closed and open maps and their compositions. The transquotient maps preserve the property of being a Polish space, and every stable map between separable metric spaces is transquotient.

In particular, a composition of closed and open maps (the intermediary spaces may not be metric) preserves the property of being a Polish space. This generalizes the results of Sierpinski and Vainstein for open and closed maps.

1.: G. Choquet, Lectures on Analysis, Volume $\mathrm{I}$ , Math. Lecture Notes Series-W.A. Benjamin, 1969. MR 40:3252
2.: G. Debs and J.Saint Raymond, Compact Covering and Game Determinacy, Topology and Appl. 68 (1996), 153-185. MR 96m:54067
3.: E. Michael, Complete spaces and tri-quotient maps, Illinois J. Math. 21(3) (1977), 716-733. MR 57:7543
4.: E. Michael, Partition-complete spaces and their preservation by tri-quotient and related maps, Top. and Appl. 73 (1996), 121-131. MR 97h:54016
5.: A. Ostrovsky, On compact-covering mappings, Soviet Math.Dokl. 17 (1976), 606-610.
6.: A. Ostrovsky, New classes of maps related to k-covering maps, Moskow University Mathematics Bulletin 49 (1994), 20-23.
7.: W. Sierpinski, Sur une propriété des ensembles $G_{\delta }$ , Fund. Math. (1930), 173-180.
8.: A.H. Stone, Metrizability of decomposition spaces, PAMS 7 (1956), 690-700. MR 19:299b
9.: I.A. Vainstein, On closed mappings of metric spaces, Dokl.Acad.Nauk USSR 57 (1947), 319-321.

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 54C10, 54D18

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS