Abstract:
Bela Kerekjarto was a Hungarian topologist active in the 1930’s. He is well-known in some quarters, but I first came across him while researching the work of Yael Naim Dowker, who taught at Imperial from the mid 1950’s until her retirement in the mid 1980’s. Some of her work, in particular with her Ph D student George Lederer, impinged on topological dynamics. Their joint work used a remarkable result of Kerekjarto which in essence shows the existence of nontrivial stable/unstable sets for any compact invariant set, some 25 years before the publication of the now-classical corresponding results for the differentiable category. I shall discuss the implications for the structure of the set of invariant sets of a homeomorphism of a compact metric space. There will be more questions than answers