Corpus ID: 15580171

A notion of graph homeomorphism

@article{Knill2014ANO,
  title={A notion of graph homeomorphism},
  author={Oliver Knill},
  journal={ArXiv},
  year={2014},
  volume={abs/1401.2819}
}
  • O. Knill
  • Published 2014
  • Mathematics, Computer Science
  • ArXiv
We introduce a notion of graph homeomorphisms which uses the concept of dimension and homotopy for graphs. It preserves the dimension of a subbasis, cohomology and Euler characteristic. Connectivity and homotopy look as in classical topology. The Brouwer-Lefshetz fixed point leads to the following discretiszation of the Kakutani fixed point theorem: any graph homeomorphism T with nonzero Lefschetz number has a nontrivial invariant open set which is fixed by T. 
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