| Title:
|
Monotone normality and extension of functions (English) |
| Author:
|
Stares, I. S. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
36 |
| Issue:
|
3 |
| Year:
|
1995 |
| Pages:
|
563-578 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We provide a characterisation of monotone normality with an analogue of the Tietze-Urysohn theorem for monotonically normal spaces as well as answer a question due to San-ou concerning the extension of Urysohn functions in monotonically normal spaces. We also extend a result of van Douwen, giving a characterisation of $K_0$-spaces in terms of semi-continuous functions, as well as answer another question of San-ou concerning semi-continuous Urysohn functions. (English) |
| Keyword:
|
monotonically normal |
| Keyword:
|
extension of functions |
| Keyword:
|
Tietze |
| Keyword:
|
Urysohn |
| Keyword:
|
$K_1$ |
| Keyword:
|
$K_0$ |
| MSC:
|
54C20 |
| MSC:
|
54D15 |
| MSC:
|
54E50 |
| idZBL:
|
Zbl 0882.54012 |
| idMR:
|
MR1364497 |
| . |
| Date available:
|
2009-01-08T18:20:12Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118785 |
| . |
| Reference:
|
[1] Borges C.J.R.: A study of monotonically normal spaces.Proc. Amer. Math. Soc. 38 (1973), 211-214. Zbl 0257.54018, MR 0324644 |
| Reference:
|
[2] van Douwen E.K.: Simultaneous extension of continuous functions.in Eric K. van Douwen, Collected Papers, Volume 1, J. van Mill, ed., North-Holland, Amsterdam, 1994. |
| Reference:
|
[3] Engelking R.: General Topology.Sigma Series in Pure Mathematics, Vol. 6, Heldermann Verlag, Berlin, 1989. Zbl 0684.54001, MR 1039321 |
| Reference:
|
[4] Gartside P.M.: Monotonicity in analytic topology.D. Phil. Thesis, Oxford University, 1993. |
| Reference:
|
[5] Gillman L., Jerison M.: Rings of continuous functions.Van Nostrand, Princeton, N.J., 1960. Zbl 0327.46040, MR 0116199 |
| Reference:
|
[6] Heath R.W., Lutzer D.J., Zenor P.L.: Monotonically normal spaces.Trans. Amer. Math. Soc. 178 (1973), 481-493. Zbl 0269.54009, MR 0372826 |
| Reference:
|
[7] Mandelkern M.: A short proof of the Tietze-Urysohn extension theorem.Arch. Math. (Basel) 60 (1993), 364-366. Zbl 0778.54005, MR 1206320 |
| Reference:
|
[8] Moody P.J., Roscoe A.W.: Acyclic monotone normality.Topology Appl. 47 (1992), 53-67. Zbl 0801.54018, MR 1189992 |
| Reference:
|
[9] San-ou S.: Characterizations of monotonically normal spaces.Questions and Answers in Gen. Top. 6 (1988), 117-123. Zbl 0672.54017, MR 1045604 |
| Reference:
|
[10] Scott B.M.: A ``more topological'' proof of the Tietze-Urysohn theorem.Amer. Math. Monthly 85 (1978), 192-193. Zbl 0376.54006, MR 0474185 |
| Reference:
|
[11] Stares I.S.: Extension of functions and generalised metric spaces.D. Phil. Thesis, Oxford University, June 1994. |
| . |
