On Generic Topological Embeddings

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2025年1月16日

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Wiesław Kubiś,
Andrzej Kucharski,
Sławomir Turek

摘要

We show that an embedding of a fixed 0-dimensional compact space K into the Čech–Stone remainder $\omega ^*$ $ω^{*}$ as a nowhere dense P-set is the unique generic limit, a special object in the category consisting of all continuous maps from K to compact metric spaces. Using categorical Fraïssé theory, we obtain some well-known theorems about Čech–Stone remainders of infinite discrete spaces. Furthermore, we prove several results concerning universality and homogeneity of the space $\kappa ^\kappa $ $κ^{κ}$ , with $\kappa $ $κ$ a regular uncountable cardinal, using generalized ultrametrics.