Displaying similar documents to “On a problem of J. Nagata”

Covering properties in countable products, II

Sachio Higuchi, Hidenori Tanaka (2006)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

In this paper, we discuss covering properties in countable products of Čech-scattered spaces and prove the following: (1) If Y is a perfect subparacompact space and { X n : n ∈ ω } is a countable collection of subparacompact Čech-scattered spaces, then the product Y × ∏ n ∈ ω X n is subparacompact and (2) If { X n : n ∈ ω } is a countable collection of metacompact Čech-scattered spaces, then the product ∏ n ∈ ω X n is metacompact.

Monotone weak Lindelöfness

Maddalena Bonanzinga, Filippo Cammaroto, Bruno Pansera (2011)

Open Mathematics

Similarity:

The definition of monotone weak Lindelöfness is similar to monotone versions of other covering properties: X is monotonically weakly Lindelöf if there is an operator r that assigns to every open cover U a family of open sets r(U) so that (1) ∪r(U) is dense in X, (2) r(U) refines U, and (3) r(U) refines r(V) whenever U refines V. Some examples and counterexamples of monotonically weakly Lindelöf spaces are given and some basic properties such as the behavior with respect to products and...