Lefschetz fixed-point theorem

Let $f:X\rightarrow X$ be a map from a compact triangulable space $X$ to itself. A point $x$ is a fixed point of $f$ if $fx=x$. Denote the Lefschetz number of $f$ by $\Lambda _{f}$. Then the Lefshetz fixed-point theorem states that if $\Lambda _{f}\neq 0$, then $f$ has a fixed point.