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'Betti number'
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| Title of object: |
Betti number |
| Canonical Name: |
BettiNumber |
| Type: |
Definition |
| Created on: |
2003-07-23 15:39:28 |
| Modified on: |
2003-07-24 11:28:53 |
| Classification: |
msc:55N10 |
| Keywords: |
homology |
Preamble:
% 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}
\usepackage{amsthm}
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%\usepackage{psfrag}
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%\usepackage{graphicx}
% for neatly defining theorems and propositions
%\usepackage{amsthm}
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%\usepackage{xypic}
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% define commands here
\newcommand{\mc}{\mathcal}
\newcommand{\mb}{\mathbb}
\newcommand{\mf}{\mathfrak}
\newcommand{\ol}{\overline}
\newcommand{\ra}{\rightarrow}
\newcommand{\la}{\leftarrow}
\newcommand{\La}{\Leftarrow}
\newcommand{\Ra}{\Rightarrow}
\newcommand{\nor}{\vartriangleleft}
\newcommand{\Gal}{\text{Gal}}
\newcommand{\GL}{\text{GL}}
\newcommand{\Z}{\mb{Z}}
\newcommand{\R}{\mb{R}}
\newcommand{\Q}{\mb{Q}}
\newcommand{\C}{\mb{C}}
\newcommand{\<}{\langle}
\renewcommand{\>}{\rangle} |
Content:
\PMlinkescapeword{rank}
Let $X$ denote a topological space, and let $H_k(X,\Z)$ denote the $k$-th homology group of $X$. If $H_k(X,\Z)$ is finitely generated, then its rank is called the $k$-th Betti number of $X$. |
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