Every weakly initially 𝔪 -compact topological space is 𝔪 pcap

Paolo Lipparini

Czechoslovak Mathematical Journal (2011)

  • Volume: 61, Issue: 3, page 781-784
  • ISSN: 0011-4642

Abstract

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The statement in the title solves a problem raised by T. Retta. We also present a variation of the result in terms of [ μ , κ ] -compactness.

How to cite

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Lipparini, Paolo. "Every weakly initially ${\mathfrak {m}}$-compact topological space is ${\mathfrak {m}}$pcap." Czechoslovak Mathematical Journal 61.3 (2011): 781-784. <http://eudml.org/doc/196323>.

@article{Lipparini2011,
abstract = {The statement in the title solves a problem raised by T. Retta. We also present a variation of the result in terms of $[\mu ,\kappa ]$-compactness.},
author = {Lipparini, Paolo},
journal = {Czechoslovak Mathematical Journal},
keywords = {weak initial compactness; $\{\mathfrak \{m\}\}$pcap; $[\mu ,\kappa ]$-compactness; pseudo-$(\kappa ,\lambda )$-compactness; covering number; weak initial compactness; pcap; -compactness; pseudo--compactness; covering number},
language = {eng},
number = {3},
pages = {781-784},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Every weakly initially $\{\mathfrak \{m\}\}$-compact topological space is $\{\mathfrak \{m\}\}$pcap},
url = {http://eudml.org/doc/196323},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Lipparini, Paolo
TI - Every weakly initially ${\mathfrak {m}}$-compact topological space is ${\mathfrak {m}}$pcap
JO - Czechoslovak Mathematical Journal
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 3
SP - 781
EP - 784
AB - The statement in the title solves a problem raised by T. Retta. We also present a variation of the result in terms of $[\mu ,\kappa ]$-compactness.
LA - eng
KW - weak initial compactness; ${\mathfrak {m}}$pcap; $[\mu ,\kappa ]$-compactness; pseudo-$(\kappa ,\lambda )$-compactness; covering number; weak initial compactness; pcap; -compactness; pseudo--compactness; covering number
UR - http://eudml.org/doc/196323
ER -

References

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  1. Arhangel'skii, A. V., 10.1016/S0166-8641(97)00220-4, Topology Appl. 89 (1998), 285-298. (1998) Zbl0932.54025MR1645188DOI10.1016/S0166-8641(97)00220-4
  2. Comfort, W. W., Negrepontis, S., Chain Conditions in Topology, Cambridge Tracts in Mathematics 79, Cambridge University Press, Cambridge-New York (1982). (1982) Zbl0488.54002MR0665100
  3. Frolík, Z., Generalisations of compact and Lindelöf spaces, Russian. English summary Czech. Math. J. 9 (1959), 172-217. (1959) MR0105075
  4. Lipparini, P., Some compactness properties related to pseudocompactness and ultrafilter convergence, Topol. Proc. 40 (2012), 29-51. (2012) MR2793281
  5. Lipparini, P., 10.1016/j.topol.2011.05.039, Topology Appl. 158 (2011), 1655-1666. (2011) MR2812474DOI10.1016/j.topol.2011.05.039
  6. Retta, T., Some cardinal generalizations of pseudocompactness, Czech. Math. J. 43 (1993), 385-390. (1993) Zbl0798.54032MR1249608
  7. Shelah, S., Cardinal Arithmetic, Oxford Logic Guides, 29, The Clarendon Press, Oxford University Press, New York (1994). (1994) Zbl0848.03025MR1318912

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