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Baireness of C k ( X ) for ordered X

Michael Granado, Gary Gruenhage (2006)

Commentationes Mathematicae Universitatis Carolinae

We show that if X is a subspace of a linearly ordered space, then C k ( X ) is a Baire space if and only if C k ( X ) is Choquet iff X has the Moving Off Property.

Base-base paracompactness and subsets of the Sorgenfrey line

Strashimir G. Popvassilev (2012)

Mathematica Bohemica

A topological space X is called base-base paracompact (John E. Porter) if it has an open base ℬ such that every base ℬ ' ⊆ ℬ has a locally finite subcover 𝒞 ⊆ ℬ ' . It is not known if every paracompact space is base-base paracompact. We study subspaces of the Sorgenfrey line (e.g. the irrationals, a Bernstein set) as a possible counterexample.

C * -points vs P -points and P ♭ -points

Jorge Martinez, Warren Wm. McGovern (2022)

Commentationes Mathematicae Universitatis Carolinae

In a Tychonoff space X , the point p ∈ X is called a C * -point if every real-valued continuous function on C ∖ { p } can be extended continuously to p . Every point in an extremally disconnected space is a C * -point. A classic example is the space 𝐖 * = ω 1 + 1 consisting of the countable ordinals together with ω 1 . The point ω 1 is known to be a C * -point as well as a P -point. We supply a characterization of C * -points in totally ordered spaces. The remainder of our time is aimed at studying when a point in a product space is a C * -point....

Combinatorial trees in Priestley spaces

Richard N. Ball, Aleš Pultr, Jiří Sichler (2005)

Commentationes Mathematicae Universitatis Carolinae

We show that prohibiting a combinatorial tree in the Priestley duals determines an axiomatizable class of distributive lattices. On the other hand, prohibiting n -crowns with n ≥ 3 does not. Given what is known about the diamond, this is another strong indication that this fact characterizes combinatorial trees. We also discuss varieties of 2-Heyting algebras in this context.

Compact pospaces

Venu G. Menon (2003)

Commentationes Mathematicae Universitatis Carolinae

Posets with property DINT which are compact pospaces with respect to the interval topologies are characterized.

Compact spaces that do not map onto finite products

Antonio Avilés (2009)

Fundamenta Mathematicae

We provide examples of nonseparable compact spaces with the property that any continuous image which is homeomorphic to a finite product of spaces has a maximal prescribed number of nonseparable factors.

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