Countable products of Čech-scattered supercomplete spaces

Aarno Hohti; Zi Qiu Yun

Czechoslovak Mathematical Journal (1999)

  • Volume: 49, Issue: 3, page 569-583
  • ISSN: 0011-4642

Abstract

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We prove by using well-founded trees that a countable product of supercomplete spaces, scattered with respect to Čech-complete subsets, is supercomplete. This result extends results given in [Alstera], [Friedlera], [Frolika], [HohtiPelantb], [Pelanta] and its proof improves that given in [HohtiPelantb].

How to cite

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Hohti, Aarno, and Yun, Zi Qiu. "Countable products of Čech-scattered supercomplete spaces." Czechoslovak Mathematical Journal 49.3 (1999): 569-583. <http://eudml.org/doc/30507>.

@article{Hohti1999,
abstract = {We prove by using well-founded trees that a countable product of supercomplete spaces, scattered with respect to Čech-complete subsets, is supercomplete. This result extends results given in [Alstera], [Friedlera], [Frolika], [HohtiPelantb], [Pelanta] and its proof improves that given in [HohtiPelantb].},
author = {Hohti, Aarno, Yun, Zi Qiu},
journal = {Czechoslovak Mathematical Journal},
keywords = {supercomplete; product spaces; Čech-complete; C-scattered; uniform space; paracompact; locally fine; product spaces; Čech-complete; -scattered; uniform space; paracompact; locally fine},
language = {eng},
number = {3},
pages = {569-583},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Countable products of Čech-scattered supercomplete spaces},
url = {http://eudml.org/doc/30507},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Hohti, Aarno
AU - Yun, Zi Qiu
TI - Countable products of Čech-scattered supercomplete spaces
JO - Czechoslovak Mathematical Journal
PY - 1999
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 49
IS - 3
SP - 569
EP - 583
AB - We prove by using well-founded trees that a countable product of supercomplete spaces, scattered with respect to Čech-complete subsets, is supercomplete. This result extends results given in [Alstera], [Friedlera], [Frolika], [HohtiPelantb], [Pelanta] and its proof improves that given in [HohtiPelantb].
LA - eng
KW - supercomplete; product spaces; Čech-complete; C-scattered; uniform space; paracompact; locally fine; product spaces; Čech-complete; -scattered; uniform space; paracompact; locally fine
UR - http://eudml.org/doc/30507
ER -

References

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  1. 10.4064/fm-114-3-173-181, Fund. Math. 114:3 (1981), 173–181 [Alstera]. (1981) Zbl0369.54005MR0644402DOI10.4064/fm-114-3-173-181
  2. On a class of spaces containing all metric and all locally bicompact spaces.-, Soviet Math. Dokl. 4 (1963), 1051–1055 [Arhangelskia]. (1963) 
  3. 10.2307/2372828, Amer. J. Math. 80 (1958), 185–190 [Corsona]. (1958) Zbl0080.15803MR0094780DOI10.2307/2372828
  4. Outline of General Topology.-, Polish Scientific Publishers, 1968 [Engelkinga]. (1968 [Engelkinga]) Zbl0157.53001MR0230273
  5. 10.2140/pjm.1987.129.277, Pacific Math. Journal 129:2 (1987), 277–296 [Friedlera]. (1987) MR0909031DOI10.2140/pjm.1987.129.277
  6. On the topological product of paracompact spaces.-, Bull. Acad. Pol. Sci. Math. 8 (1960), 747–750 [Frolika]. (1960) MR0125559
  7. Generalizations of G δ -property of complete metric spaces.-, Czechoslovak Math. J. 10 (85) (1960), 359–379 [Frolikb]. (1960) MR0116305
  8. Locally G δ -spaces.-, Czechoslovak Math. J. 12 (87) (1962), 346–354 [Frolikc]. (1962) MR0148028
  9. 10.2307/2040492, Proc. Amer. Math. Soc. 46:1 (1974), 111–119 [Frolikd]. (1974) MR0358704DOI10.2307/2040492
  10. 10.1090/S0002-9947-1959-0112119-4, Trans. Amer. Math. Soc. 93 (1959), 145–168 [Ginsburga]. (1959) MR0112119DOI10.1090/S0002-9947-1959-0112119-4
  11. Some nearly fine uniform spaces.-, Proc. London Math. Soc. (3), 28 (1974), 517–546 [Hagera]. (1974) Zbl0284.54017MR0397670
  12. 10.4064/fm-16-1-353-360, Fund. Math. 16 (1930), 353–360 [Hausdorffa]. (1930) DOI10.4064/fm-16-1-353-360
  13. On uniform paracompactness.-, Ann. Acad. Scient. Fenn., Series A, I. Mathematica, Dissertationes 36 (1981 [Hohtia]). (1981 [Hohtia]) Zbl0502.54021MR0625526
  14. 10.1090/S0002-9939-1983-0684658-8, Proc. Amer. Math. Soc. 87 (1983), 557–560 [Hohtib]. (1983) Zbl0538.54015MR0684658DOI10.1090/S0002-9939-1983-0684658-8
  15. 10.2140/pjm.1984.111.39, Pacific J. Math. 111 (1) (1984), 39–48 [Hohtic]. (1984) Zbl0558.54020MR0732057DOI10.2140/pjm.1984.111.39
  16. On supercomplete uniform spaces II.-, Czechoslovak Math. J. 37 (1987), 376–385 [Hohtid]. (1987) Zbl0654.54020MR0904765
  17. 10.1090/S0002-9939-1986-0835894-1, Proc. Amer. Math. Soc. 97:2, 339–342 [Hohtie]. MR0835894DOI10.1090/S0002-9939-1986-0835894-1
  18. 10.4064/fm-125-2-133-142, Fund. Math. CXXV (1985), 133–142 [HohtiPelanta]. (1985) MR0813750DOI10.4064/fm-125-2-133-142
  19. 10.4064/fm-136-2-115-120, Fund. Math. 136:2 (1990), 115–120 [HohtiPelantb]. (1990) MR1074656DOI10.4064/fm-136-2-115-120
  20. 10.1016/0166-8641(87)90081-2, Topology Appl. 25 (1987), 245–252 [Huseka]. (1987) MR0889869DOI10.1016/0166-8641(87)90081-2
  21. 10.2140/pjm.1962.12.287, Pacific J. Math. 12 (1962), 287–290 [Isbella]. (1962) Zbl0104.39503MR0156311DOI10.2140/pjm.1962.12.287
  22. Uniform spaces.-, Math. Surveys, no. 12, Amer. Math. Soc., Providence, R. I., 1964 [Isbellb]. (1964 [Isbellb]) Zbl0124.15601MR0170323
  23. An Introduction to Intersection Homology Theory.-, Pitman Research Notes in Mathematics Series 187, Longman, 1988 [Kirwana]. (1988 [Kirwana]) Zbl0656.55002MR0981185
  24. 10.1090/S0002-9904-1963-10931-3, Bull. Amer. Math. Soc. 69 (1963), 375–376 [Michaela]. (1963) Zbl0114.38904MR0152985DOI10.1090/S0002-9904-1963-10931-3
  25. On the dimension of rectangular products.-, Sov. Math. Dokl. 16 (1975), 344–347 [Pasynkova]. (1975) Zbl0334.54024MR0377833
  26. Locally fine uniformities and normal covers.-, Czechoslovak Math. J. 37 (112) (1987), 181–187 [Pelanta]. (1987) Zbl0656.54020MR0882592
  27. 10.1090/S0002-9939-1977-0436085-3, Proc. Amer. Math. Soc. 62:2 (1977), 359–362 [Ricea]. (1977) Zbl0353.54011MR0436085DOI10.1090/S0002-9939-1977-0436085-3
  28. 10.1090/S0002-9939-1983-0715885-9, Proc. Amer. Math. Soc. 89:3 (1983), 551–552 [Rudina]. (1983) MR0715885DOI10.1090/S0002-9939-1983-0715885-9
  29. 10.1090/S0002-9947-1963-0151935-0, Trans. Amer. Math. Soc. 107 (1963), 58–70 [Stonea]. (1963) Zbl0114.38604MR0151935DOI10.1090/S0002-9947-1963-0151935-0
  30. 10.4064/fm-73-1-59-74, Fund. Math. 73 (1971), 59–74 [Telgarskya]. (1971) MR0295293DOI10.4064/fm-73-1-59-74
  31. Spaces defined by topological games.-, Fund. Math. LXXXVIII:3 (1975), 193–223 [Telgarskyb]. (1975) 

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