Displaying similar documents to ““More or less' first-return recoverable functions.”

An abstract version of Sierpiński's theorem and the algebra generated by A and CA functions

J. Cichoń, Michał Morayne (1993)

Fundamenta Mathematicae

Similarity:

We give an abstract version of Sierpiński's theorem which says that the closure in the uniform convergence topology of the algebra spanned by the sums of lower and upper semicontinuous functions is the class of all Baire 1 functions. Later we show that a natural generalization of Sierpiński's result for the uniform closure of the space of all sums of A and CA functions is not true. Namely we show that the uniform closure of the space of all sums of A and CA functions is a proper subclass...

Derivative and antiderivative operators and the size of complex domains

Luis Bernal-González (1994)

Annales Polonici Mathematici

Similarity:

We prove some conditions on a complex sequence for the existence of universal functions with respect to sequences of certain derivative and antiderivative operators related to it. These operators are defined on the space of holomorphic functions in a complex domain. Conditions for the equicontinuity of those sequences are also studied. The conditions depend upon the size of the domain.

Algebras of Borel measurable functions

Michał Morayne (1992)

Fundamenta Mathematicae

Similarity:

We determine the size levels for any function on the hyperspace of an arc as follows. Assume Z is a continuum and consider the following three conditions: 1) Z is a planar AR; 2) cut points of Z have component number two; 3) any true cyclic element of Z contains at most two cut points of Z. Then any size level for an arc satisfies 1)-3) and conversely, if Z satisfies 1)-3), then Z is a diameter level for some arc.

Fragmentability and σ-fragmentability

J. Jayne, I. Namioka, C. Rogers (1993)

Fundamenta Mathematicae

Similarity:

Recent work has studied the fragmentability and σ-fragmentability properties of Banach spaces. Here examples are given that justify the definitions that have been used. The fragmentability and σ-fragmentability properties of the spaces ℓ ∞ and ℓ c ∞ ( Γ ) , with Γ uncountable, are determined.

Uniformly completely Ramsey sets

Udayan Darji (1993)

Colloquium Mathematicae

Similarity:

Galvin and Prikry defined completely Ramsey sets and showed that the class of completely Ramsey sets forms a σ-algebra containing open sets. However, they used two definitions of completely Ramsey. We show that they are not equivalent as they remarked. One of these definitions is a more uniform property than the other. We call it the uniformly completely Ramsey property. We show that some of the results of Ellentuck, Silver, Brown and Aniszczyk concerning completely Ramsey sets also...