Editing Lefschetz fixed-point theorem (section)

==Relation to the Brouwer fixed-point theorem==
The Lefschetz fixed-point theorem generalizes the [[Brouwer fixed-point theorem]],<ref name="brouwer-1910">{{cite journal | last1 = Brouwer | first1 = L. E. J. | author-link = Luitzen Egbertus Jan Brouwer | year = 1911| title = Über Abbildungen von Mannigfaltigkeiten | url = http://resolver.sub.uni-goettingen.de/purl?GDZPPN002264021 | journal = [[Mathematische Annalen]] | volume = 71 | pages = 97–115 | doi = 10.1007/BF01456931 | s2cid = 177796823 | language = de }}</ref> which states that every continuous map from the <math>n</math>-dimensional [[unit disk|closed unit disk]] <math>D^n</math> to <math>D^n</math> must have at least one fixed point.

This can be seen as follows: <math>D^n</math> is compact and triangulable, all its homology groups except <math>H_0</math> are zero, and every continuous map <math>f\colon D^n \to D^n</math> induces the identity map <math>f_* \colon H_0(D^n, \Q) \to H_0(D^n, \Q)</math>, whose trace is one; all this together implies that <math>\Lambda_f</math> is non-zero for any continuous map <math>f\colon D^n \to D^n</math>.