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W3137019376 abstract "We develop the theory of Fraisse 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 Fraisse Frechet space and we use the Fraisse correspondence in this setting to obtain many examples of such spaces. This allows us to give a Fraisse-theoretic construction of $(mathbb{G}^omega, (|cdot|_n)_{n<omega})$, the separable Frechet space of almost universal disposition for the class of all finite-dimensional Frechet spaces with an infinite sequence of seminorms. We then identify and prove an approximate Ramsey property for various classes of finite-dimensional multi-seminormed spaces using known approximate Ramsey properties of normed spaces. A version of the Kechris-Pestov-Todorcevic correspondence for approximately ultrahomogeneous Frechet spaces is also established and is used to obtain new examples of extremely amenable groups. In particular, we show that the group of surjective linear seminorm-preserving isometries of $(mathbb{G}^omega, (|cdot|_n)_{n<omega})$ is extremely amenable." @default.
W3137019376 created "2021-03-29" @default.
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W3137019376 creator A5003444852 @default.
W3137019376 date "2021-03-19" @default.
W3137019376 modified "2023-09-27" @default.
W3137019376 title "Fraiss'e and Ramsey properties of Fr'echet spaces" @default.
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