Український математичний конгрес - 2009
Алексей Довгошей (Институт прикладной математики и механики НАН Украины, Донецк, Украина)
Some properties of tangent spaces to metric spaces
The recent achievements in the metric space theory are closely related to some generalizations of differentiation. See, for instance, the concept of weak gradient  or Cheeger's notion of differentiability for Rademacher's theorem in certain metric measure spaces .
A tangent space to an arbitrary metric space X at a point p from X was defined in  as a factor space of some family of sequences of points of X which converge to p. This approach makes possible to define a metric space valued derivative of functions f from X to Y, X and Y are metric spaces, as mappings between tangent spaces to X and, respectively, to Y .
In the lecture will be discussed some examples of tangent spaces to metric spaces and, moreover, will be described the metric spaces which have bounded or proper or compact tangent spaces  and metric spaces having ultrametric tangent spaces .