Source: J. Math. Soc. Japan Volume 61, Number 4
(2009), 1293-1301.
Generalizing the Ohio completeness property, we introduce the notion of $\kappa$-Ohio completeness. Although many results from a previous paper by the authors may easily be adapted for this new property, there are also some interesting differences. We provide several examples to illustrate this. We also have a consistency result; depending on the value of the cardinal $\mathfrak{d}$, the countable union of open and $\omega_{1}$-Ohio complete subspaces may or may not be $\omega_{1}$-Ohio complete.
References
A. V. Arhangel'skiĭ, Remainders in compactifications and generalized metrizability properties, Topology Appl., 150 (2005), 79–90.
D. Basile and J. van Mill, Ohio completeness and products, Topology Appl., 155 (2008), 180–189.
D. Basile and J. van Mill, and G. J. Riddderbos, Sum theorems for Ohio completeness, Colloq. Math., 113 (2008), 91–104.
J. Chaber, Metacompactness and the class MOBI, Fund. Math., 91 (1976), 211–217.
Mathematical Reviews (MathSciNet):
MR415561
E. K. van Douwen, The integers and topology, Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 111–167.
Mathematical Reviews (MathSciNet):
MR776622
R. Engelking, General topology, second ed., Sigma Series in Pure Mathematics, 6, Heldermann Verlag, Berlin, 1989, Translated from the Polish by the author.
T. Jech, Set theory, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2003, The third millennium edition, revised and expanded.
A. Landver, Baire numbers, uncountable Cohen sets and perfect-set forcing, J. Symbolic Logic, 57 (1992), no. 3, 1086–1107.
O. Okunev and A. Tamariz-Mascarúa, On the Čech number of $C_{p}(X)$, Topology Appl., 137 (2004), 237–249, IV Iberoamerican Conference on Topology and its Applications.