Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Tychonoff reflection in products and the $ \omega$-topology on function spaces

Author: Stephen Watson
Journal: Proc. Amer. Math. Soc. 108 (1990), 557-559
MSC: Primary 54C35; Secondary 54B10, 54D45
MathSciNet review: 1007518
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We show that if $ X$ is a topological space such that $ CR(X)$, the topology on $ X$ generated by the cozero sets, is not locally compact, then there is a regular space $ Y$ such that $ CR(X \times Y) \ne CR(X) \times CR(Y)$. We use the $ \omega $-topology on the space of continuous functions $ C\left( {X,Y} \right)$ (where $ \omega $ is an open cover of $ X$) which was defined by Arens and Dugundji in 1950.

References [Enhancements On Off] (What's this?)

  • [1] Richard Arens and James Dugundji, Topologies for function spaces, Pacific J. Math. 1 (1951), 5-31. MR 0043447 (13:264d)
  • [2] Shinpei Oka, Tychonoff functor and product spaces, Proc. Japan Acad. 54A(4) (1978), 97-100. MR 0482671 (58:2729)
  • [3] Petr Simon, Completely regular modification and products, Comment. Math. Univ. Carolina 25(1) (1984), 121-128. MR 749120 (86j:54033)
  • [4] A. Tychonoff, Über die topologische Erweiterung von Räumen, Math. Ann. 102 (1930), 544-561. MR 1512595
  • [5] Paul Urysohn, Über die Mächtigkeit der zusammenhängenden Mengen, Math. Ann. 94 (1925), 262-295. MR 1512258

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54C35, 54B10, 54D45

Retrieve articles in all journals with MSC: 54C35, 54B10, 54D45

Additional Information

Article copyright: © Copyright 1990 American Mathematical Society

American Mathematical Society