On Generic Topological Embeddings

We show that an embedding of a fixed 0-dimensional compact space K into the & Ccaron;ech-Stone remainder omega & lowast;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega <^>*$$\end{document} 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 Fra & iuml;ss & eacute; theory, we obtain some well-known theorems about & Ccaron;ech-Stone remainders of infinite discrete spaces. Furthermore, we prove several results concerning universality and homogeneity of the space kappa kappa\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa <^>\kappa $$\end{document}, with kappa\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa $$\end{document} a regular uncountable cardinal, using generalized ultrametrics.