Article
Full entry |
PDF
(0.1 MB)
Feedback
PDF
(0.1 MB)
Feedback
Keywords:
clopen set; clopen box; Cartesian product of spaces
clopen set; clopen box; Cartesian product of spaces
Summary:
The results concern clopen sets in products of topological spaces. It is shown that a clopen subset of the product of two separable metrizable (or locally compact) spaces is not always a union of clopen boxes. It is also proved that any clopen subset of the product of two spaces, one of which is compact, can always be represented as a union of clopen boxes.
References:
[ARH] Arhangel'skii A.: private communications. 1999.
[BAU] Bauer A.: private communications. 2000.
[ENG] Engelking R.: General Topology. Sigma Series in Pure Mathematics 6, Heldermann, Berlin, revised ed., 1989. MR 1039321 | Zbl 0684.54001
[KUN] Kunen K.: private communications. 2000.
[STE] Stephenson R.M.: Product space and the Stone-Weierstrass theorem. General Topology Appl. 3 (1973), 77-79. MR 0315669
[SHO] Shostak A.: On a class of spaces containing all bicompacts and all connected spaces. in General Topology and its Relations to Modern Analysis and Algebra, Proceeding of the Forth Prague Topological Symposium, Vol. B, 1976.
[SaS] Steprans J., Shostak A.: Restricted compactness properties and their preservation under products. Topology Appl. 11 (2000), 213-229. MR 1733805 | Zbl 0962.54020
Search
Partner of
