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Modes of ideal continuity and the additive property in the Riesz space setting
-
Antonio Boccuto
,
Xenofon Dimitriou
Published/Copyright:
May 1, 2014
Abstract.
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.
Keywords: (Admissible) ideal; additive property; ideal convergence/divergence; ideal continuity; modes of continuity
MSC: 28A33; 28B10; 40A35; 54A20; 54H11; 06E15; 22A05; 22A10; 28A12; 28B15; 28C15; 40C05; 40G15; 41A35; 41A36; 54E15
Funding source: University of Athens
Funding source: University of Łódź
Funding source: University of Perugia
Our thanks to the referees for their helpful suggestions.
Received: 2012-12-17
Revised: 2013-5-30
Accepted: 2013-6-7
Published Online: 2014-5-1
Published in Print: 2014-6-1
© 2014 by Walter de Gruyter Berlin/Boston
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Keywords for this article
(Admissible) ideal;
additive property;
ideal convergence/divergence;
ideal continuity;
modes of continuity
Articles in the same Issue
- Frontmatter
- Porosity and the bounded linear regularity property
- Analytic in planar domains functions with preassigned asymptotic set
- Multiplication of the distributions (x±i0)z
- Hermite–Hadamard type inequalities for extended s-convex functions on the co-ordinates in a rectangle
- Modes of ideal continuity and the additive property in the Riesz space setting
- On complex Fermi curves of two-dimensional, periodic Schrödinger operators
- On the geometrical properties of some classes of complex harmonic functions defined by analytic or coefficient conditions with complex parameter
- On the order of weighted approximation of unbounded functions by some generalizations of Gadjiev–Ibragimov operators
- On series whose rearrangements possess discrete sets of limit points
- A system of two conservation laws with flux conditions and small viscosity
