| Title:
|
A metrizable completely regular ordered space (English) |
| Author:
|
Künzi, Hans-Peter A. |
| Author:
|
Watson, Stephen |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
35 |
| Issue:
|
4 |
| Year:
|
1994 |
| Pages:
|
773-778 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We construct a completely regular ordered space $(X,{\Cal T},\leq)$ such that $X$ is an $I$-space, the topology $\Cal T$ of $X$ is metrizable and the bitopological space $(X,{\Cal T}^\sharp,{\Cal T}^{\flat})$ is pairwise regular, but not pairwise completely regular. (Here ${\Cal T}^\sharp$ denotes the upper topology and ${\Cal T}^\flat$ the lower topology of $X$.) (English) |
| Keyword:
|
completely regular ordered |
| Keyword:
|
strictly completely regular ordered |
| Keyword:
|
pairwise completely regular |
| Keyword:
|
pairwise regular |
| Keyword:
|
$I$-space |
| MSC:
|
06F30 |
| MSC:
|
54E15 |
| MSC:
|
54E55 |
| MSC:
|
54F05 |
| idZBL:
|
Zbl 0812.54038 |
| idMR:
|
MR1321247 |
| . |
| Date available:
|
2009-01-08T18:15:02Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118718 |
| . |
| Reference:
|
[1] Kelly J.C.: Bitopological spaces.Proc. London Math. Soc. 13 (1963), 71-89. Zbl 0107.16401, MR 0143169 |
| Reference:
|
[2] Künzi H.P.A.: Completely regular ordered spaces.Order 7 (1990), 283-293. MR 1113204 |
| Reference:
|
[3] Künzi H.P.A.: Quasi-uniform spaces - eleven years later.Top. Proc. 18 (1993), to appear. MR 1305128 |
| Reference:
|
[4] Lane E.P.: Bitopological spaces and quasi-uniform spaces.Proc. London Math. Soc. 17 (1967), 241-256. Zbl 0152.21101, MR 0205221 |
| Reference:
|
[5] Lawson J.D.: Order and strongly sober compactifications.in: Topology and Category Theory in Computer Science, ed. G.M. Reed, A.W. Roscoe and R.F. Wachter, Clarendon Press, Oxford, 1991, pp. 179-205. Zbl 0745.54012, MR 1145775 |
| Reference:
|
[6] Nachbin L.: Topology and Order.D. van Nostrand, Princeton, 1965. Zbl 0333.54002, MR 0219042 |
| Reference:
|
[7] Priestley H.A.: Ordered topological spaces and the representation of distributive lattices.Proc. London Math. Soc. 24 (1972), 507-530. Zbl 0323.06011, MR 0300949 |
| Reference:
|
[8] Schwarz F., Weck-Schwarz S.: Is every partially ordered space with a completely regular topology already a completely regular partially ordered space?.Math. Nachr. 161 (1993), 199-201. MR 1251017 |
| . |
