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Journals and Conferences
A functional representation of the hyperspace monad, based on the semilattice structure of function space, is constructed.
We prove addition and subspace theorems for asymptotic large inductive dimension. We investigate a transfinite extension of this dimension and show that it is trivial. 0. Asymptotic dimension asdim of a metric space was defined by Gromov for studying asymptotic invariants of discrete groups . This dimension can be considered as asymptotic analogue of the… (More)
We prove that a transfinite extension of asymptotic dimension asind is trivial. We introduce a transfinite extension of asymptotic dimension asdim and give an example of metric proper space which has transfinite infinite dimension. 0. Asymptotic dimension asdim of a metric space was defined by Gromov for studying asymptotic invariants of discrete groups… (More)
It is shown that a barycentrically soft compactum is necessarily an absolute retract of weight ≤ ω1. Since softness of a map is the mapping version of the property of a space to be an absolute retract, the above mentioned result can be considered as mapping version of the Ditor–Haydon Theorem stating that if P (X) is an absolute retract then the compactum X… (More)
We investigate some topological properties of a normal functor H introduced earlier by Radul which is a certain functorial compactification of the HartmanMycielski construction HM . We show that H is open and find the condition when HX is an absolute retract homeomorphic to the Tychonov cube.
Let F be a monad in the category Comp. We build for each F-algebra a convexity in general sense (see van de Vel 1993). We investigate properties of such convexities and apply them to prove that the multiplication map of the orderpreserving functional monad is soft.
(compacta) and continuous mappings was founded by Shchepin [Sh]. He described some elementary properties of such functors and defined the notion of the normal functor which has become very fruitful. The classes of all normal and weakly normal functors include many classical constructions: the hyperspace exp, the space of probability measures P, the… (More)