| Title:
|
Topological calculus for separating points from closed sets by maps (English) |
| Author:
|
Gutiérrez García, Javier |
| Author:
|
Kubiak, Tomasz |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
62 |
| Issue:
|
1 |
| Year:
|
2012 |
| Pages:
|
257-264 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Pointfree formulas for three kinds of separating points for closed sets by maps are given. These formulas allow controlling the amount of factors of the target product space so that it does not exceed the weight of the embeddable space. In literature, the question of how many factors of the target product are needed for the embedding has only been considered for specific spaces. Our approach is algebraic in character and can thus be viewed as a contribution to Kuratowski's topological calculus. (English) |
| Keyword:
|
embedding |
| Keyword:
|
separating points from closed sets |
| Keyword:
|
weak separating points from closed sets |
| Keyword:
|
separating family |
| Keyword:
|
weight |
| MSC:
|
54A25 |
| MSC:
|
54C25 |
| idZBL:
|
Zbl 1249.54035 |
| idMR:
|
MR2899749 |
| DOI:
|
10.1007/s10587-012-0010-0 |
| . |
| Date available:
|
2012-03-05T07:30:21Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142055 |
| . |
| Reference:
|
[1] Engelking, R.: General Topology.Tom 60. Warszawa: PWN---Polish Scientific Publishers 626 (1977). Zbl 0373.54002, MR 0500780 |
| Reference:
|
[2] Español, L., García, J. Gutiérrez, Kubiak, T.: Separating families of locale maps and localic embeddings.Algebra Univers (2012). MR 2898718 |
| Reference:
|
[3] Chattopadhyay, K. C., Ghosh, D. P., Guin, S.: An embedding theorem and its consequences.Rocky Mt. J. Math. 22 (1992), 1277-1282. Zbl 0795.54023, MR 1201091, 10.1216/rmjm/1181072654 |
| Reference:
|
[4] Johnstone, P. T.: Stone Spaces.Cambridge Studies in Advanced Mathematics, 3. Cambridge etc.: Cambridge University Press (1986), 370. Zbl 0586.54001, MR 0861951 |
| Reference:
|
[5] Kubiak, T.: On $L$-Tychonoff spaces.Fuzzy Sets Syst. 73 (1995), 25-53. Zbl 0867.54005, MR 1355356 |
| Reference:
|
[6] Kubiak, T.: On $L$-Tychonoff spaces II.Fuzzy Sets Syst. 182 (2011), 21-36. MR 2825771 |
| Reference:
|
[7] Kuratowski, K.: Topology, Vol. I.New York-London: Academic Press; Warszawa: PWN---Polish Scientific Publishers. XX 560 (1966). Zbl 0158.40901, MR 0217751 |
| Reference:
|
[8] Lane, S. Mac, Moerdijk, I.: Sheaves in Geometry and Logic: A First Introduction to Topos Theory.New York etc.: Springer-Verlag 627 (1992). MR 1300636 |
| Reference:
|
[9] Mrówka, S.: Further results on $E$-compact spaces.Acta Math. 120 (1968), 161-185. Zbl 0179.51202, MR 0226576, 10.1007/BF02394609 |
| Reference:
|
[10] Sherman, D.: Variations on Kuratowski's 14-set theorem.Am. Math. Mon. 117 (2010), 113-123. Zbl 1210.54004, MR 2590191, 10.4169/000298910X476031 |
| Reference:
|
[11] Sikorski, R.: Closure algebras.Fundam. Math. 36 (1949), 165-206. Zbl 0040.25204, MR 0036286, 10.4064/fm-36-1-165-206 |
| Reference:
|
[12] Tychonoff, A.: Über die topologische Erweiterung von Räumen.Math. Ann. 102 (1929), 544-561. MR 1512595, 10.1007/BF01782364 |
| . |
