| Title:
|
Pointwise and order convergence for spaces of continuous functions and spaces of Baire functions (English) |
| Author:
|
Tucker, C. T. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
34 |
| Issue:
|
4 |
| Year:
|
1984 |
| Pages:
|
562-569 |
| . |
| Category:
|
math |
| . |
| MSC:
|
46A40 |
| MSC:
|
46E05 |
| MSC:
|
54C40 |
| idZBL:
|
Zbl 0584.46016 |
| idMR:
|
MR764438 |
| DOI:
|
10.21136/CMJ.1984.101982 |
| . |
| Date available:
|
2008-06-09T15:02:27Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/101982 |
| . |
| Reference:
|
[1] C. D. Aliprantis, E. Langford: Almost $\sigma$-Dedekind complete Riesz spaces and the main inclusion theorem.Proc. Amer. Math. Soc, 44 (1974), 421 - 426. Zbl 0286.46010, MR 0346475 |
| Reference:
|
[2] V. M. Bogdan: Measurability and linear lattices of real functions closed under convergence everywhere.Bull. Acad. Polon. Sci., Sér. Sci. Math. Astronom. Phys., 20 (1972), 982-986. MR 0313776 |
| Reference:
|
[3] D. H. Fremlin: Riesz spaces with the order-continuity property I.Math. Proc. Cambridge Phil. Soc, 81 (1977), 31-42. Zbl 0344.46019, MR 0425572, 10.1017/S0305004100000244 |
| Reference:
|
[4] L. Gillman, M. Henrikson: Concerning rings of continuous functions.Trans. Amer. Math. Soc, 77 (1954), pp. 340-362. MR 0063646, 10.1090/S0002-9947-1954-0063646-5 |
| Reference:
|
[5] C. B. Huijsmans, B. de Pagter: On z-ideals and d-ideals in Riesz spaces.11, Indag. Math. 42 (Proc Netherl. Acad. Sc. A 83), (1980), 391-408. Zbl 0451.46003, MR 0597997 |
| Reference:
|
[6] W. A. J. Luxemburg, A. С Zaanen: Riesz Spaces I.(North-Holland, Amsterdam, 1971). |
| Reference:
|
[7] R. D. Mauldin: On the Baire system generated by a linear lattice of functions.Fund. Math., 68 (1910), 51-59. MR 0273363, 10.4064/fm-68-1-51-59 |
| Reference:
|
[8] R. D. Mauldin: Baire functions, Borel sets and ordinary function systems.Advances Math., 72 (1974), 418-450. Zbl 0278.26005, MR 0367911, 10.1016/S0001-8708(74)80011-3 |
| Reference:
|
[9] P. R. Meyer: The Baire order problem for compact spaces.Duke Math. J., 33 (1966), 33 - 40. Zbl 0138.17602, MR 0190897, 10.1215/S0012-7094-66-03305-9 |
| Reference:
|
[10] M. Meyer: Une nouvelle caractérisation des espaces vectoriels réticulés presque $\sigma$-complets.CR. Acad. Sc Paris (287) A, 1081-1084. Zbl 0394.46006, MR 0520409 |
| Reference:
|
[11] F. Papangelou: Order convergence and topological completion of commutative latticegroups.Math. Ann., 155 (1964), 81-107. MR 0174498, 10.1007/BF01344076 |
| Reference:
|
[12] J. Quinn: Intermediate Riesz spaces.Pacific J. Math., 56 (1975), 225-263. Zbl 0315.06009, MR 0380355, 10.2140/pjm.1975.56.225 |
| Reference:
|
[13] G. Regoli: Some characterizations of sets of measurable functions.Amer. Math. Month., 84 (1977), 455-458. Zbl 0389.28001, MR 0447513, 10.1080/00029890.1977.11994383 |
| Reference:
|
[14] С. T. Tucker: Limit of a sequence of functions with only countably many points of discontinuity.Proc. Amer. Math. Soc., 19 (1968), 118-122. Zbl 0157.20302, MR 0219029, 10.1090/S0002-9939-1968-0219029-3 |
| Reference:
|
[15] C. T. Tucker: Homomorphisms of Riesz spaces.Pacific J. Math., 55 (1974), 289-300. Zbl 0315.06007, MR 0369208, 10.2140/pjm.1974.55.289 |
| Reference:
|
[16] С. T. Tucker: Riesz homomorphisms and positive linear maps.Pacific J. Math., 69 (1977), 551-556. Zbl 0332.46006, MR 0438180, 10.2140/pjm.1977.69.551 |
| Reference:
|
[17] С. T. Tucker: Representation of Baire functions as continuous functions.Fund. Math., 101 (1978), 181-188. Zbl 0448.54014, MR 0521120, 10.4064/fm-101-3-181-188 |
| Reference:
|
[18] С. T. Tucker: Positive operators on spaces of Baire functions.Illinois J. Math., 25 (1981), 295-301. Zbl 0437.46021, MR 0607031, 10.1215/ijm/1256047262 |
| . |
