Fremlin tensor product behaves well with the unbounded order convergence

2023/09/01 by Zabeti, Omid
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2309.00301

Abstract

Suppose Σ is a topological space and S(Σ) is the vector lattice of all equivalent classes of continuous real-valued functions defined on open dense subsets of Σ. In this paper, we establish some lattice and topological aspects of S(Σ). In particular, as an application, we show that the unbounded order convergence and the order convergence are stable under passing to the Fremlin tensor product of two Archimedean vector lattices.

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