Displaying similar documents to “Monotone meta-Lindelöf spaces”

Monotone weak Lindelöfness

Maddalena Bonanzinga, Filippo Cammaroto, Bruno Pansera (2011)

Open Mathematics

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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...

Notes on monotone Lindelöf property

Ai-Jun Xu, Wei-Xue Shi (2009)

Czechoslovak Mathematical Journal

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We provide a necessary and sufficient condition under which a generalized ordered topological product (GOTP) of two GO-spaces is monotonically Lindelöf.

A note on monotone countable paracompactness

Ge Ying, Chris Good (2001)

Commentationes Mathematicae Universitatis Carolinae

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We show that a space is MCP (monotone countable paracompact) if and only if it has property ( * ) , introduced by Teng, Xia and Lin. The relationship between MCP and stratifiability is highlighted by a similar characterization of stratifiability. Using this result, we prove that MCP is preserved by both countably biquotient closed and peripherally countably compact closed mappings, from which it follows that both strongly Fréchet spaces and q-space closed images of MCP spaces are MCP. Some...

On monotone Lindelöfness of countable spaces

Ronnie Levy, Mikhail Matveev (2008)

Commentationes Mathematicae Universitatis Carolinae

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A space is monotonically Lindelöf (mL) if one can assign to every open cover 𝒰 a countable open refinement r ( 𝒰 ) so that r ( 𝒰 ) refines r ( 𝒱 ) whenever 𝒰 refines 𝒱 . We show that some countable spaces are not mL, and that, assuming CH, there are countable mL spaces that are not second countable.