Abstract
The real-valued bounded normal upper semicontinuous functions on a topological space X were introduced by Dilworth (Trans Am Math Soc 68:427–438, 1950). The aim of this paper is to show that the set of all normal upper (lower) semicontinuous functions on a completely regular topological space \({X}\) can be endowed with an algebraic structure and lattice operations such that it becomes a Dedekind complete Riesz space that is the Dedekind completion of C b (X), the Riesz space of all bounded continuous functions on X. The Dedekind completion of C(X) is also obtained.
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Dăneţ, N. Riesz Spaces of Normal Semicontinuous Functions. Mediterr. J. Math. 12, 1345–1355 (2015). https://doi.org/10.1007/s00009-014-0466-2
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DOI: https://doi.org/10.1007/s00009-014-0466-2