Geodesic
Closed ideals and closed congruences of semirings of $[0,1]$-valued functions with topology of pointwise convergence
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 3, pp. 83-93 Cet article a éte moissonné depuis la source Math-Net.Ru

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For an arbitrary Tychonoff space $X$, we describe closed ideals and closed congruences of the topological semiring $C_p(X,\mathbf I)$ of all continuous functions on $X$ with values in the closed unit interval $\mathbf I$ considered in the topology of pointwise convergence. The duality between the category of Tychonoff spaces $X$ with continuous mappings and the category of topological semirings $C_p(X,\mathbf I)$ with continuous homomorphisms preserving constants is established.
Keywords: semiring, continuous function, Tychonoff topology, closed ideal, closed congruence, duality. 
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E. M. Vechtomov; E. N. Lubyagina. Closed ideals and closed congruences of semirings of $[0,1]$-valued functions with topology of pointwise convergence. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 3, pp. 83-93. http://geodesic.mathdoc.fr/item/TIMM_2013_19_3_a7/

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