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Ramsey, Lebesgue, and Marczewski sets and the Baire property

Patrick Reardon (1996)

Fundamenta Mathematicae

We investigate the completely Ramsey, Lebesgue, and Marczewski σ-algebras and their relations to the Baire property in the Ellentuck and density topologies. Two theorems concerning the Marczewski σ-algebra (s) are presented. THEOREM. In the density topology D, (s) coincides with the σ-algebra of Lebesgue measurable sets. THEOREM. In the Ellentuck topology on ${[ω]}^{ω}$ , ${(s)}_{0}$ is a proper subset of the hereditary ideal associated with (s). We construct an example in the Ellentuck topology of a set which is...

Real-valued continuous functions and the span of continua

A. Lelek, L. Mohler (1975)

Colloquium Mathematicae

Real-valued functions on Alexandroff (zero-set) spaces

Anthony W. Hager (1975)

Commentationes Mathematicae Universitatis Carolinae

Real-valued functions on certain semi-metric spaces

Harold R. Bennett (1975)

Compositio Mathematica

Regular representations of semisimple MV-algebras by continuous real functions

Ján Jakubík (2001)

Mathematica Slovaca

Remark on the Abstract Dirichlet Problem for Baire-One Functions

Ondřej F. K. Kalenda (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

We study the possibility of extending any bounded Baire-one function on the set of extreme points of a compact convex set to an affine Baire-one function and related questions. We give complete solutions to these questions within a class of Choquet simplices introduced by P. J. Stacey (1979). In particular we get an example of a Choquet simplex such that its set of extreme points is not Borel but any bounded Baire-one function on the set of extreme points can be extended to an affine Baire-one function....

Remarks on $L B I$ -subalgebras of $C (X)$

Mehdi Parsinia (2016)

Commentationes Mathematicae Universitatis Carolinae

Let $A (X)$ denote a subalgebra of $C (X)$ which is closed under local bounded inversion, briefly, an $L B I$ -subalgebra. These subalgebras were first introduced and studied in Redlin L., Watson S., Structure spaces for rings of continuous functions with applications to realcompactifications, Fund. Math. 152 (1997), 151–163. By characterizing maximal ideals of $A (X)$ , we generalize the notion of $z_{A}^{β}$ -ideals, which was first introduced in Acharyya S.K., De D., An interesting class of ideals in subalgebras of $C (X)$ containing...

Representation of Baire functions as continuous functions

C. Tucker (1978)

Fundamenta Mathematicae

Rings Of Real-Valued Functions And The Finite Subcovering Property.

Alexander Abian, Sergio Salbany (1979)

Revista colombiana de matematicas

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