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Homotopy theory, homological algebra, algebraic treatments of manifolds.
8
votes
Accepted
Homotopy type of the Hausdorff metric
In J. Andres, M. Väth, Calculation of Lefschetz and Nielsen Numbers in Hyperspaces for Fractals and Dynamical Systems, Proc. Amer. Math. Soc. 135 (2007), 479-487, it was shown (esssentially, the resul …
2
votes
What do absolute neighborhood retracts look like?
For Euclidean neighborhood retracts, there is the nice characterization of being locally connected (and locally compact). Unfortunately, in the infinite-dimensional case, locally connectedness is nece …