Article
Keywords:
weak initial compactness; ${\mathfrak m}$pcap; $[\mu ,\kappa ]$-compactness; pseudo-$(\kappa ,\lambda )$-compactness; covering number
Summary:
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.
References:
[2] Comfort, W. W., Negrepontis, S.:
Chain Conditions in Topology. Cambridge Tracts in Mathematics 79, Cambridge University Press, Cambridge-New York (1982).
MR 0665100 |
Zbl 0488.54002
[3] Frolík, Z.:
Generalisations of compact and Lindelöf spaces. Russian. English summary Czech. Math. J. 9 (1959), 172-217.
MR 0105075
[4] Lipparini, P.:
Some compactness properties related to pseudocompactness and ultrafilter convergence. Topol. Proc. 40 (2012), 29-51.
MR 2793281
[6] Retta, T.:
Some cardinal generalizations of pseudocompactness. Czech. Math. J. 43 (1993), 385-390.
MR 1249608 |
Zbl 0798.54032
[7] Shelah, S.:
Cardinal Arithmetic. Oxford Logic Guides, 29, The Clarendon Press, Oxford University Press, New York (1994).
MR 1318912 |
Zbl 0848.03025