Rough convergence on Riesz spaces
Abdullah Ayd{\i}n, Mehmet K\"u\c{c}\"ukaslan, Mokhwetha Mabula

TL;DR
This paper generalizes the concept of rough convergence to Riesz spaces, introducing a new form of convergence for nets that accounts for a fixed roughness degree, and explores its properties and implications.
Contribution
It develops the theory of rough $ ext{c}$-convergence in Riesz spaces, establishing its axioms, properties, and relationship with order boundedness and limit points.
Findings
Rough $ ext{c}$-convergence satisfies formal convergence axioms
The set of limit points may be non-unique
Order boundedness relates to non-empty limit point sets
Abstract
This paper extends the theory of rough convergence from normed linear spaces to the more abstract setting of Riesz spaces. We introduce and systematically develop the concept of rough -convergence (-convergence) for nets. A net in a Riesz space is said to be rough -convergent to if there exists a net in with for a given background convergence , such that holds for all , where is a fixed positive vector in representing the roughness degree. The study first establishes that this new construction satisfies the axioms of a formal convergence structure. Key properties of -convergence are then investigated, including its relationship with linearity and the…
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