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Σ -products of paracompact Čech-scattered spaces

Hidenori Tanaka (2006)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we shall discuss Σ -products of paracompact Čech-scattered spaces and show the following: (1) Let Σ be a Σ -product of paracompact Čech-scattered spaces. If Σ has countable tightness, then it is collectionwise normal. (2) If Σ is a Σ -product of first countable, paracompact (subparacompact) Čech-scattered spaces, then it is shrinking (subshrinking).

Σ s -products revisited

Reynaldo Rojas-Hernández (2015)

Commentationes Mathematicae Universitatis Carolinae

We show that any Σ s -product of at most 𝔠 -many L Σ ( ≤ ω ) -spaces has the L Σ ( ≤ ω ) -property. This result generalizes some known results about L Σ ( ≤ ω ) -spaces. On the other hand, we prove that every Σ s -product of monotonically monolithic spaces is monotonically monolithic, and in a similar form, we show that every Σ s -product of Collins-Roscoe spaces has the Collins-Roscoe property. These results generalize some known results about the Collins-Roscoe spaces and answer some questions due to Tkachuk [Lifting the Collins-Roscoe...

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