File:Mutual embedding of open and closed real unit interval.pdf
Summary
| Description |
English: Mutual injective embeddings of open interval (0,1) ⊆ ℝ and the closed interval [0,1] ⊆ ℝ. In both directions, the mapping x ↦ 94x+3/100 is used. |
| Date | |
| Source | Own work |
| Author | Jochen Burghardt |
| Other versions | File:Mutual embedding of open and closed real unit interval.pdf - File:Mutual embedding of open and closed real unit interval svg.svg |
LaTeX source |
|---|
\documentclass[12pt]{article}
\usepackage[pdftex]{color}
\usepackage[paperwidth=105mm,paperheight=35mm]{geometry}
\setlength{\topmargin}{-36mm}
\setlength{\textwidth}{105mm}
\setlength{\textheight}{35mm}
\setlength{\oddsidemargin}{-23mm}
\setlength{\parindent}{0cm}
\setlength{\unitlength}{1mm}
\pagestyle{empty}
\definecolor{cOC} {rgb}{0.50,0.00,0.00} % mapping open-->closed
\definecolor{cCO} {rgb}{0.00,0.50,0.00} % mapping closed-->open
\definecolor{cC} {rgb}{0.70,0.99,0.70} % image of open interval
\definecolor{cO} {rgb}{0.99,0.70,0.70} % image of closed interval
\begin{document}
\begin{picture}(100,30)
% image of open interval
\textcolor{cO}{\put(3.000,25.000){\line(1,0){94.000}}}%
\textcolor{cO}{\put(2.700,25.000){\makebox(0.000,0.000)[l]{\scriptsize (}}}%
\textcolor{cO}{\put(97.300,25.000){\makebox(0.000,0.000)[r]{\scriptsize )}}}%
% image of closed interval
\textcolor{cC}{\put(3.000,9.000){\line(1,0){94.000}}}%
\textcolor{cC}{\put(2.700,9.000){\makebox(0.000,0.000)[l]{\scriptsize [}}}%
\textcolor{cC}{\put(97.300,9.000){\makebox(0.000,0.000)[r]{\scriptsize ]}}}%
% embedding open --> closed
\textcolor{cOC}{\put(0.000,11.000){\vector(1,4){3.000}}}%
\textcolor{cOC}{\put(100.000,11.000){\vector(-1,4){3.000}}}%
% embedding open --> closed
\textcolor{cCO}{\put(0.000,23.000){\vector(1,-4){3.000}}}%
\textcolor{cCO}{\put(100.000,23.000){\vector(-1,-4){3.000}}}%
\thicklines
% coordinates
\put(-0.600,1.000){\makebox(0.000,0.000)[l]{0}}%
\put(100.600,1.000){\makebox(0.000,0.000)[r]{1}}%
% open interval
\put(0.000,6.000){\line(1,0){100.000}}%
\put(-0.600,6.000){\makebox(0.000,0.000)[l]{\bf (}}%
\put(100.600,6.000){\makebox(0.000,0.000)[r]{\bf )}}%
% closed interval
\put(0.000,28.000){\line(1,0){100.000}}%
\put(-0.600,28.000){\makebox(0.000,0.000)[l]{\bf [}}%
\put(100.600,28.000){\makebox(0.000,0.000)[r]{\bf ]}}%
\end{picture}
\end{document}
|
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.