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Corpus ID: 218487086

Brouwer fixed point theorem as a corollary of Lawvere

@article{McCallum2020BrouwerFP,
title={Brouwer fixed point theorem as a corollary of Lawvere},
author={R. McCallum},
journal={arXiv: Logic},
year={2020}
}

It is investigated in what sense the Brouwer fixed point theorem may be viewed as a corollary of the Lawvere fixed point theorem. A suitable generalisation of the Lawvere fixed point theorem is found and a means is identified by which the Brouwer fixed point theorem can be shown to be a corollary, once an appropriate continuous surjective mapping $A' \rightarrow X^{A''}$ has been constructed for each space $X$ in a certain class of "nice" spaces for each one of which the exponential topology on… CONTINUE READING