Pointwise and order convergence for spaces of continuous functions and spaces of Baire functions

C. T. Tucker

Czechoslovak Mathematical Journal (1984)

  • Volume: 34, Issue: 4, page 562-569
  • ISSN: 0011-4642

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Tucker, C. T.. "Pointwise and order convergence for spaces of continuous functions and spaces of Baire functions." Czechoslovak Mathematical Journal 34.4 (1984): 562-569. <http://eudml.org/doc/13480>.

@article{Tucker1984,
author = {Tucker, C. T.},
journal = {Czechoslovak Mathematical Journal},
keywords = {monotone pointwise convergence; monotone order convergence; bounded pointwise convergence; spaces of continuous functions; spaces of Baire functions; Riesz homomorphism; P-space},
language = {eng},
number = {4},
pages = {562-569},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Pointwise and order convergence for spaces of continuous functions and spaces of Baire functions},
url = {http://eudml.org/doc/13480},
volume = {34},
year = {1984},
}

TY - JOUR
AU - Tucker, C. T.
TI - Pointwise and order convergence for spaces of continuous functions and spaces of Baire functions
JO - Czechoslovak Mathematical Journal
PY - 1984
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 34
IS - 4
SP - 562
EP - 569
LA - eng
KW - monotone pointwise convergence; monotone order convergence; bounded pointwise convergence; spaces of continuous functions; spaces of Baire functions; Riesz homomorphism; P-space
UR - http://eudml.org/doc/13480
ER -

References

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  1. C. D. Aliprantis, E. Langford, Almost σ -Dedekind complete Riesz spaces and the main inclusion theorem, Proc. Amer. Math. Soc, 44 (1974), 421 - 426. (1974) Zbl0286.46010MR0346475
  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. (1972) MR0313776
  3. D. H. Fremlin, 10.1017/S0305004100000244, Math. Proc. Cambridge Phil. Soc, 81 (1977), 31-42. (1977) Zbl0344.46019MR0425572DOI10.1017/S0305004100000244
  4. L. Gillman, M. Henrikson, 10.1090/S0002-9947-1954-0063646-5, Trans. Amer. Math. Soc, 77 (1954), pp. 340-362. (1954) MR0063646DOI10.1090/S0002-9947-1954-0063646-5
  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. (1980) Zbl0451.46003MR0597997
  6. W. A. J. Luxemburg, A. С Zaanen, Riesz Spaces I, (North-Holland, Amsterdam, 1971). (1971) 
  7. R. D. Mauldin, On the Baire system generated by a linear lattice of functions, Fund. Math., 68 (1910), 51-59. (1910) MR0273363
  8. R. D. Mauldin, 10.1016/S0001-8708(74)80011-3, Advances Math., 72 (1974), 418-450. (1974) Zbl0278.26005MR0367911DOI10.1016/S0001-8708(74)80011-3
  9. P. R. Meyer, 10.1215/S0012-7094-66-03305-9, Duke Math. J., 33 (1966), 33 - 40. (1966) Zbl0138.17602MR0190897DOI10.1215/S0012-7094-66-03305-9
  10. M. Meyer, Une nouvelle caractérisation des espaces vectoriels réticulés presque σ -complets, CR. Acad. Sc Paris (287) A, 1081-1084. Zbl0394.46006MR0520409
  11. F. Papangelou, 10.1007/BF01344076, Math. Ann., 155 (1964), 81-107. (1964) MR0174498DOI10.1007/BF01344076
  12. J. Quinn, 10.2140/pjm.1975.56.225, Pacific J. Math., 56 (1975), 225-263. (1975) Zbl0315.06009MR0380355DOI10.2140/pjm.1975.56.225
  13. G. Regoli, 10.2307/2321903, Amer. Math. Month., 84 (1977), 455-458. (1977) Zbl0389.28001MR0447513DOI10.2307/2321903
  14. С. T. Tucker, 10.1090/S0002-9939-1968-0219029-3, Proc. Amer. Math. Soc., 19 (1968), 118-122. (1968) Zbl0157.20302MR0219029DOI10.1090/S0002-9939-1968-0219029-3
  15. C. T. Tucker, 10.2140/pjm.1974.55.289, Pacific J. Math., 55 (1974), 289-300. (1974) Zbl0315.06007MR0369208DOI10.2140/pjm.1974.55.289
  16. С. T. Tucker, 10.2140/pjm.1977.69.551, Pacific J. Math., 69 (1977), 551-556. (1977) Zbl0332.46006MR0438180DOI10.2140/pjm.1977.69.551
  17. С. T. Tucker, Representation of Baire functions as continuous functions, Fund. Math., 101 (1978), 181-188. (1978) Zbl0448.54014MR0521120
  18. С. T. Tucker, Positive operators on spaces of Baire functions, Illinois J. Math., 25 (1981), 295-301. (1981) Zbl0437.46021MR0607031

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