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Choice Functions for Complexes and for Filters

Speaker

Ron Aharoni, Technion, Israel Institute of Technology

Time

2018.09.10 14:30-15:30

Venue

Middle Lecture Room, Math Building

Abstract

A family C of sets is called a complex if is a closed down, namely α∈C, β⊆α imply β∈C. Similarly, a filter is a family of sets that is closed up. Many combinatorial and geometric problems can be formulated in the language of choice functions whose range is required to belong to a given complex, or to a given filter. Surprisingly, topology, in particular fixed point theorems, can help in finding such choice functions.