CantorSpace 2003-07-10 20:57:39 2005-03-18 22:20:43 Definition Cantor Polish space binary sequence language % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here The {\it Cantor space}, denoted by $\mathbb{C}$ is the set of all infinite binary sequences with the product topology. It is a perfect Polish space. It is a compact subspace of the Baire space, the set of all infinite sequences of integers (again with the natural product topology). {\bf References.} \begin{itemize} \item Moschovakis, Yiannis N. \emph{Descriptive Set Theory}. North-Holland Pub. Co. 1980, Amsterdam; New York. \end{itemize}