Geodesic
A Counterexample in Finite Fixed Point Theory
Canadian mathematical bulletin, Tome 22 (1979) no. 1, pp. 99-100

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This note answers a question raised by Lee Mohler in 1970, by exhibiting a finite topological space X which is the union of closed subspaces Y, Z, such that Y, Z, and Y ⋂ Z, but not X, have the fixed point property. The example is a triangulation △ of S3, the points of X being the simplices of Δ and the closed sets the subcomplexes of △. 
Enos, H. C. A Counterexample in Finite Fixed Point Theory. Canadian mathematical bulletin, Tome 22 (1979) no. 1, pp. 99-100. doi: 10.4153/CMB-1979-014-6
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     title = {A {Counterexample} in {Finite} {Fixed} {Point} {Theory}},
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