The -topology and incompactness of
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
We present a forcing construction of a Hausdorff zero-dimensional Lindelöf space whose square is again Lindelöf but its cube has a closed discrete subspace of size , hence the Lindelöf degree . In our model the Continuum Hypothesis holds true. After that we give a description of a forcing notion to get a space such that for all positive integers , but .
A note on Boolean algebras
We show that splitting of elements of an independent family of infinite regular size will produce a full size independent set.
AB-compacta
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