% \iffalse meta-comment % % Copyright (C) 2018 - 2021 by ChairX % % This file may be distributed and/or modified under the % conditions of the LaTeX Project Public License, either % version 1.3 of this license or (at your option) any later % version. The latest version of this license is in: % % http://www.latex-project.org/lppl.txt % % and version 1.3 or later is part of all distributions of % LaTeX version 2005/12/01 or later. % % This file contains the documentation of all topology related macros . % % Macros have to be described by (delete the first %) % \DescribeMacro{\macro} % Description and usage of the macro. % % The description will appear in the usage % part of the documentation. Use \subsubsection{} etc. for structuring. % % The implementation of the macros defined here has to be written in % chairxmathTopology.dtx %\fi % %\subsubsection{Macros for Topology} % % \DescribeMacro{\cl} % Topological closure |X^\cl|: $X^\cl$\\ % Uses |scriptfont|. % % \DescribeMacro{\scl} % Sequential closure |A^\scl|: $A^\scl$\\ % Uses |scriptfont|. % % \DescribeMacro{\interior} % Open interior |A^\interior|: $A^\interior$ % % \DescribeMacro{\boundary} % Boundary of a subset |\boundary A|: $\boundary A$ % % \DescribeMacro{\supp} % Support of a function |\supp f|: $\supp f$\\ % Uses |operatorfont|. % % \DescribeMacro{\dist} % Distance |\dist(p, A)|: $\dist(p, A)$\\ % Uses |operatorfont|. % % \DescribeMacro{\topology} % Font for topology |\topology{M}|: $\topology{M}$\\ % Uses |topologyfont|. % % \DescribeMacro{\filter} % Font for filter |\filter{F}|: $\filter{F}$\\ % Uses |filterfont|. % % \DescribeMacro{\sheaf} % Font for sheaves |\sheaf{F}|: $\sheaf{F}$\\ % Uses |sheaffont|. % % \DescribeMacro{\Sections} % Discontinuous sections of a presheaf |\Sections(\sheaf{F})|: $\Sections(\sheaf{F})$\\ % Uses |operatorfont|. % % \DescribeMacro{\HOM} % Sheaf of morphisms between sheaves |\HOM(\sheaf{F}, \sheaf{G})|: $\HOM(\sheaf{F}, \sheaf{G})$\\ % Uses |sheaffont| and |\mathit|. % % \DescribeMacro{\etale} % Étalé space of presheaf |\etale{\sheaf{F}}|: $\etale{\sheaf{F}}$. % % % \subsubsection{Categories from Topology} % % \DescribeMacro{\topological} % Category of topological spaces |\topological|: $\topological$ \\ % Uses |categoryname|. % % \DescribeMacro{\Topological} % Category of Hausdorff topological spaces |\Topological|: $\Topological$ \\ % Uses |categoryname|. % % \DescribeMacro{\Sheaves} % Category of sheaves over a space |\Sheaves(M)|: $\Sheaves(M)$ \\ % Uses |categoryname|. % % \DescribeMacro{\PreSheaves} % Category of presheaves over a space |\PreSheaves(M)|: $\PreSheaves(M)$ \\ % Uses |categoryname|. % % \DescribeMacro{\Etale} % Category of étalé spaces over a space |\Etale(M)|: $\Etale(M)$ \\ % Uses |categoryname|.