| Title:
|
On a class of real normed lattices (English) |
| Author:
|
Alegre, C. |
| Author:
|
Ferrer, J. |
| Author:
|
Gregori, V. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
48 |
| Issue:
|
4 |
| Year:
|
1998 |
| Pages:
|
785-792 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We say that a real normed lattice is quasi-Baire if the intersection of each sequence of monotonic open dense sets is dense. An example of a Baire-convex space, due to M. Valdivia, which is not quasi-Baire is given. We obtain that $E$ is a quasi-Baire space iff $(E, T({\mathcal U}),T({\mathcal U}^{-1}))$, is a pairwise Baire bitopological space, where $\mathcal U$, is a quasi-uniformity that determines, in $L$. Nachbin’s sense, the topological ordered space $E$. (English) |
| Keyword:
|
Barrelled space |
| Keyword:
|
convex-Baire space |
| Keyword:
|
normed lattice |
| Keyword:
|
pairwise Baire spaces |
| Keyword:
|
quasi-Baire spaces |
| Keyword:
|
quasi-uniformity |
| MSC:
|
54E15 |
| MSC:
|
54E52 |
| MSC:
|
54E55 |
| MSC:
|
54F05 |
| idZBL:
|
Zbl 0949.54045 |
| idMR:
|
MR1658273 |
| . |
| Date available:
|
2009-09-24T10:18:26Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127454 |
| . |
| Reference:
|
[1] Ferrando, J.C.; Ferrer, J.: On certain non barrelled normed spaces.Math. Japonica 38 (1993), 161–164. MR 1204194 |
| Reference:
|
[2] Ferrer, J; Gregori, V; Alegre, C.: Quasi-uniform structures in linear lattices.Rocky Mountain J. Math. (1994), 877–884. MR 1245452 |
| Reference:
|
[3] Fletcher, P.; Lindgren, W.F.: Quasi-uniform Spaces.Marcel Dekker Inc. New York, 1982. MR 0660063 |
| Reference:
|
[4] Kelly, J,C.: Bitopological spaces.Proc. London Math. Soc. (3) 13 (1963), 71–89. Zbl 0107.16401, MR 0143169 |
| Reference:
|
[5] Nachbin, L.: Topology and Order.Robert E. Kriegler Publishing Co., Huntington, New York, 1976. Zbl 0333.54002, MR 0415582 |
| Reference:
|
[6] Valdivia, M.: Topics in Locally Convex Spaces.North-Holland, Amsterdam, 1982. Zbl 0489.46001, MR 0671092 |
| . |
