Fraïssé and Ramsey properties of Fréchet spaces

2021/03/19 by Kawach, Jamal K., López-Abad, Jordi
#05D10 (Primary) 46A04 #37B05 #46A61 #46B20 #46M40 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #Functional Analysis (math.FA) #Logic (math.LO)

paper · doi:10.48550/arxiv.2103.11049

Abstract

We develop the theory of Fraïssé limits for classes of finite-dimensional multi-seminormed spaces, which are defined to be vector spaces equipped with a finite sequence of seminorms. We define a notion of a Fraïssé Fréchet space and we use the Fraïssé correspondence in this setting to obtain many examples of such spaces. This allows us to give a Fraïssé-theoretic construction of (\mathbbG^ω, (‖⋅‖_n)_n

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