In this paper we present some different types of ideal convergence/divergence and of ideal continuity for Riesz space-valued functions, and prove some basic properties and comparison results. We investigate the relations among different modes of ideal continuity and present a characterization of the (AP)-property for ideals of an abstract set Λ. Finally we pose some open problems.
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In this paper we deal with continuous convergence and some related properties of sequences of functions. We present some conditions to get uniform convergence of the sequence involved to a constant function. As an application, we give a result on equivalence between modes of convergence.
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