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37 votes
14 answers
5k views

What are interesting families of subsets of a given set?

Motivation The usual starting point of both Topology and Measure Theory is the definition of a family of subsets of a set $S$. Indeed, one defines a topology on $S$ to be a family of subsets ...
18 votes
8 answers
2k views

Concepts in topology successfully transferred to graph theory and combinatorics with non-trivial applications?

What are some of the difficult concepts in topology that have been transferred to graph theory and combinatorics where a certain new application has been found. A good example is Lovász's proof of ...