| Title:
|
Decreasing (G) spaces (English) |
| Author:
|
Stares, Ian |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
39 |
| Issue:
|
4 |
| Year:
|
1998 |
| Pages:
|
809-817 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider the class of decreasing (G) spaces introduced by Collins and Roscoe and address the question as to whether it coincides with the class of decreasing (A) spaces. We provide a partial solution to this problem (the answer is yes for homogeneous spaces). We also express decreasing (G) as a monotone normality type condition and explore the preservation of decreasing (G) type properties under closed maps. The corresponding results for decreasing (A) spaces are unknown. (English) |
| Keyword:
|
decreasing (G) |
| Keyword:
|
decreasing (A) |
| Keyword:
|
homogeneous |
| Keyword:
|
monotone normality |
| Keyword:
|
closed map |
| MSC:
|
54C10 |
| MSC:
|
54D70 |
| MSC:
|
54E20 |
| idZBL:
|
Zbl 1060.54508 |
| idMR:
|
MR1715469 |
| . |
| Date available:
|
2009-01-08T18:48:54Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119055 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Collins P.J., Roscoe A.W.: Criteria for metrisability.Proc. Amer. Math. Soc. 90 (1984), 631-640. Zbl 0541.54034, MR 0733418 |
| Reference:
|
[4] Collins P.J., Reed G.M., Roscoe A.W., Rudin M.E.: A lattice of conditions on topological spaces.Proc. Amer. Math. Soc. 94 (1985), 487-496. Zbl 0562.54043, MR 0787900 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[9] Moody P.J., Reed G.M., Roscoe A.W., Collins P.J.: A lattice of conditions on topological spaces II.Fund. Math. 138 (1991), 69-81. Zbl 0745.54008, MR 1124537 |
| Reference:
|
[10] Moody P.J., Roscoe A.W.: Acyclic monotone normality.Topology Appl. 47 (1992), 53-67. Zbl 0801.54018, MR 1189992 |
| Reference:
|
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| . |
