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Topological Vector Spaces
Preface In the notion of a topological vector space, there is a very nice interplay between the algebraic structure of a vector space and a topology on the space, basically so that the vector space
Analysis of and on uniformly rectifiable sets
The notion of uniform rectifiability of sets (in a Euclidean space), which emerged only recently, can be viewed in several different ways. It can be viewed as a quantitative and scale-invariant
Fractured fractals and broken dreams : self-similar geometry through metric and measure
1. Basic definitions 2. Examples 3. Comparison 4. The Heisenberg group 5. Background information 6. Stronger self-similarity for BPI spaces 7. BPI equivalence 8. Convergence of metric spaces 9. Weak
Finding curves on general spaces through quantitative topology, with applications to Sobolev and Poincaré inequalities
In many metric spaces one can connect an arbitrary pair of points with a curve of finite length, but in Euclidean spaces one can connect a pair of points with a lot of rectifiable curves, curves that
Quasiconformal mappings and chord-arc curves
Given a quasiconformal mapping p on the plane, what conditions on its dilatation , guarantee that p(R) is rectifiable and PIR is locally abso lutely continuous? We show in this paper that if ,
On the nonexistence of bilipschitz parameterizations and geometric problems about $A_\infty$-weights
How can one recognize when a metric space is bilipschitz equivalent to an Euclidean space? One should not take the abstraction of metric spaces too seriously here; subsets of Rn are already quite
Good metric spaces without good parameterizations
A classical problem in geometric topology is to recognize when a topological space is a topological manifold. This paper addresses the question of when a metric space admits a quasisymmetric