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A note on weakly ϱ-upper continuous functions

Nowakowska K., Turowska M.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2014

Vol. 19

195--206

In the article we present definition and some properties of weakly ϱ-upper continuous functions. We find maximal additive and maximal multiplicative families for the class of weakly ϱ-upper continuous functions.

Maximal classes for rho-upper continuous functions

Kowalczyk S., Nowakowska K.

Journal of Applied Analysis

2013

Vol. 19, nr 1

69--89

In this paper we present some properties of ρ-upper continuous functions. We give a condition equivalent to ρ-upper continuity and find maximal additive and maximal multiplicative classes for the family of ρ-upper continuous functions. These classes depend on whether ρ<1 or ρ=1. To describe maximal additive and maximal multiplicative classes for 1-upper continuous function, we need the notions of sparsity and T*topology.

On weakly measurable functions

Żeberski S.

Bulletin of the Polish Academy of Sciences. Mathematics

2005

Vol. 53, no 4

421-428

We show that if T is an uncountable Polish space, X is a metrizable space and f : T → X is a weakly Baire measurable function, then we can find a meagre set M ⊆ T such that f [T ∖ M] is a separable space. We also give an example showing that “metrizable” cannot be replaced by “normal”.