Dimension Axiom

One of the Eilenberg-Steenrod Axioms. Let $X$ be a single point space. $H_n(X)=0$ unless $n=0$, in which case $H_0(X)=G$ where $G$ are some Groups. The $H_0$ are called the Coefficients of the Homology Theory $H(\cdot)$.

See also Eilenberg-Steenrod Axioms, Homology (Topology)