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Decreasing (G) spaces

Ian Stares (1998)

Commentationes Mathematicae Universitatis Carolinae

We consider the class of decreasing (G) spaces introduced by Collins and Roscoe and address the question as to whether it coincides with the class of decreasing (A) spaces. We provide a partial solution to this problem (the answer is yes for homogeneous spaces). We also express decreasing (G) as a monotone normality type condition and explore the preservation of decreasing (G) type properties under closed maps. The corresponding results for decreasing (A) spaces are unknown.

Definable completeness

Marta Bunge, Mamumka Jibladze, Thomas Streicher (2004)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Diagonals and discrete subsets of squares

Dennis Burke, Vladimir Vladimirovich Tkachuk (2013)

Commentationes Mathematicae Universitatis Carolinae

In 2008 Juhász and Szentmiklóssy established that for every compact space X there exists a discrete D X × X with | D | = d ( X ) . We generalize this result in two directions: the first one is to prove that the same holds for any Lindelöf Σ -space X and hence X ω is d -separable. We give an example of a countably compact space X such that X ω is not d -separable. On the other hand, we show that for any Lindelöf p -space X there exists a discrete subset D X × X such that Δ = { ( x , x ) : x X } D ¯ ; in particular, the diagonal Δ is a retract of D ¯ and the projection...

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