Fixed Points in Digital Topology (via Helly Posets)
Rueiher Tsaur, Michael B. Smyth · Electronic Notes in Theoretical Computer Science · 2003
We extend some of our previous results on fixed points of graph multifunctions to posets. The posets of most interest here are the (finite) Khalimsky spaces, in their specialization order. Retracts of Khalimsky spaces coincide with Helly posets. Notions of convexity can be defined in these spaces, providing the basis for certain “geometric” fixed point theorems.