Geodesic
The topological Riesz algebras
Filomat, Tome 36 (2022) no. 7, p. 2325

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DOI

The multiplicative order convergence was studied and investigated on Riesz algebras. This paper deals with Riesz algebras and different topologies on them. In this paper, we investigate Riesz algebras on which we define various kinds of continuities. We give the relation between them under certain specific conditions. We show some relations among locally full, locally convex and locally solid Riesz algebras. Also, we introduce the notions of order and topological continuity of algebraic multiplications on topological Riesz algebras. Also, we extend the multiplication to quotient spaces of Riesz algebras.
DOI : 10.2298/FIL2207325A
Classification : 06B35, 46A40, 06F15, 06F20
Keywords: Riesz algebra, locally solid Riesz algebra, locally full Riesz algebra, topological lattice-ordered group, Riesz space, f -algebra 
Abdullah Aydın; Hatice Ünlü Eroğlu; Sabahattin Ilbıra. The topological Riesz algebras. Filomat, Tome 36 (2022) no. 7, p. 2325 . doi: 10.2298/FIL2207325A
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     author = {Abdullah Ayd{\i}n and Hatice \"Unl\"u Ero\u{g}lu and Sabahattin Ilb{\i}ra},
     title = {The topological {Riesz} algebras},
     journal = {Filomat},
     pages = {2325 },
     year = {2022},
     volume = {36},
     number = {7},
     doi = {10.2298/FIL2207325A},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2207325A/}
}
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