EUDML

Currently displaying 1 – 4 of 4

Order by Relevance | Title | Year of publication

The $G_{δ}$ -topology and incompactness of $ω^{α}$

Isaac Gorelic — 1996

Commentationes Mathematicae Universitatis Carolinae

We establish a relation between covering properties (e.gĿindelöf degree) of two standard topological spaces (Lemmas 4 and 5). Some cardinal inequalities follow as easy corollaries.

On powers of Lindelöf spaces

Isaac Gorelic — 1994

Commentationes Mathematicae Universitatis Carolinae

We present a forcing construction of a Hausdorff zero-dimensional Lindelöf space $X$ whose square $X^{2}$ is again Lindelöf but its cube $X^{3}$ has a closed discrete subspace of size $𝔠^{+}$ , hence the Lindelöf degree $L (X^{3}) = 𝔠^{+}$ . In our model the Continuum Hypothesis holds true. After that we give a description of a forcing notion to get a space $X$ such that $L (X^{n}) = ℵ_{0}$ for all positive integers $n$ , but $L (X^{ℵ_{0}}) = 𝔠^{+} = ℵ_{2}$ .