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.
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.
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