LΣ(≤ ω)-spaces and spaces of continuous functions

Israel Lara; Oleg Okunev

Open Mathematics (2010)

  • Volume: 8, Issue: 4, page 754-762
  • ISSN: 2391-5455

Abstract

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We present a few results and problems related to spaces of continuous functions with the topology of pointwise convergence and the classes of LΣ(≤ ω)-spaces; in particular, we prove that every Gul’ko compact space of cardinality less or equal to 𝔠 is an LΣ(≤ ω)-space.

How to cite

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Israel Lara, and Oleg Okunev. "LΣ(≤ ω)-spaces and spaces of continuous functions." Open Mathematics 8.4 (2010): 754-762. <http://eudml.org/doc/269123>.

@article{IsraelLara2010,
abstract = {We present a few results and problems related to spaces of continuous functions with the topology of pointwise convergence and the classes of LΣ(≤ ω)-spaces; in particular, we prove that every Gul’ko compact space of cardinality less or equal to \[ \mathfrak \{c\} \] is an LΣ(≤ ω)-space.},
author = {Israel Lara, Oleg Okunev},
journal = {Open Mathematics},
keywords = {Lindelöf Σ-spaces; Pointwise convergence; Compact-valued mappings; Gul’ko compact spaces; Lindelöf -spaces; pointwise convergence; compact-valued mappings; Gul'ko compact spaces},
language = {eng},
number = {4},
pages = {754-762},
title = {LΣ(≤ ω)-spaces and spaces of continuous functions},
url = {http://eudml.org/doc/269123},
volume = {8},
year = {2010},
}

TY - JOUR
AU - Israel Lara
AU - Oleg Okunev
TI - LΣ(≤ ω)-spaces and spaces of continuous functions
JO - Open Mathematics
PY - 2010
VL - 8
IS - 4
SP - 754
EP - 762
AB - We present a few results and problems related to spaces of continuous functions with the topology of pointwise convergence and the classes of LΣ(≤ ω)-spaces; in particular, we prove that every Gul’ko compact space of cardinality less or equal to \[ \mathfrak {c} \] is an LΣ(≤ ω)-space.
LA - eng
KW - Lindelöf Σ-spaces; Pointwise convergence; Compact-valued mappings; Gul’ko compact spaces; Lindelöf -spaces; pointwise convergence; compact-valued mappings; Gul'ko compact spaces
UR - http://eudml.org/doc/269123
ER -

References

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  1. [1] Arhangel’skĭ A.V., Factorization theorems and function spaces: stability and monolithicity, Soviet Math. Dokl., 1982, 26(1), 177–181 
  2. [2] Arhangel’skĭ A.V., Topological Function Spaces, Kluwer, Dordrecht, 1992 
  3. [3] Casarrubias Segura F., Okunev O., Paniagua Ramírez C.G., Some results on LΣ(κ)-spaces, Comment. Math. Univ. Carolin., 2008, 49(4), 667–675 Zbl1212.54075
  4. [4] Engelking R., On the double circumference of Alexandroff, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys., 1968, 16(8), 629–634 Zbl0167.21001
  5. [5] Engelking R., General Topology, Sigma Series in Pure Mathematics, 6, Heldermann Verlag, Berlin, 1989 
  6. [6] Kubiś W., Okunev O., Szeptycki P.J., On some classes of Lindelöf Σ-spaces, Topology Appl., 2006, 153(14), 2574–2590 http://dx.doi.org/10.1016/j.topol.2005.09.009[WoS][Crossref] Zbl1102.54028
  7. [7] Nagami K., Σ-spaces, Fund. Math., 1969, 65, 169–192 
  8. [8] Okunev O., A method for constructing examples of M-equivalent spaces, Topology Appl. 1990, 36(2), 157–171, Correction: Topology Appl., 1993, 49(2), 191-192 http://dx.doi.org/10.1016/0166-8641(90)90006-N[Crossref] Zbl0707.54007
  9. [9] Okunev O., On Lindelöf Σ-spaces of continuous functions in the pointwise topology, Topology Appl., 1993, 49(2), 149–166 http://dx.doi.org/10.1016/0166-8641(93)90041-B[Crossref] 
  10. [10] Okunev O., Tamano K., Lindelöf powers and products of function spaces, Proc. Amer. Math. Soc., 1996, 124(9), 2905–2916 http://dx.doi.org/10.1090/S0002-9939-96-03629-5[Crossref] Zbl0858.54013
  11. [11] Simon P., On continuous image of Eberlein compacts, Comment. Math. Univ. Carolinae, 1976, 17(1), 179–194 Zbl0322.54014
  12. [12] Sokolov G.A., On some classes of compact spaces lying in Σ-products, Comment. Math. Univ. Carolinae, 1984, 25(2), 219–231 Zbl0577.54014
  13. [13] Tkachuk V.V., A glance at compact spaces which map “nicely” onto the metrizable ones, Topology Proc., 1994, 19, 321–334 Zbl0854.54022

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