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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  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
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