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Factoring Continuous Homomorphisms Defined on Submonoids of Products of Topologized Monoids

Department of Mathematics, Universidad Autónoma Metropolitana, Av. San Rafael Atlixco 186, Col. Vicentina, Del. Iztapalapa, Mexico City C.P. 09340, Mexico
Axioms 2019, 8(3), 86; https://doi.org/10.3390/axioms8030086
Received: 13 June 2019 / Revised: 19 July 2019 / Accepted: 22 July 2019 / Published: 26 July 2019
(This article belongs to the Collection Topological Groups)
We study factorization properties of continuous homomorphisms defined on submonoids of products of topologized monoids. We prove that if S is an ω-retractable submonoid of a product D = i I D i of topologized monoids and f : S H is a continuous homomorphism to a topologized semigroup H with ψ ( H ) ω , then one can find a countable subset E of I and a continuous homomorphism g : p E ( S ) H satisfying f = g p E S , where p E is the projection of D to i E D i . The same conclusion is valid if S contains the Σ -product Σ D D . Furthermore, we show that in both cases, there exists the smallest by inclusion subset E I with the aforementioned properties. View Full-Text
Keywords: monoid; homomorphism; character; factorization monoid; homomorphism; character; factorization
MDPI and ACS Style

Tkachenko, M. Factoring Continuous Homomorphisms Defined on Submonoids of Products of Topologized Monoids. Axioms 2019, 8, 86.

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