8 research outputs found
Discrete homogeneity and ends of manifolds
It is shown that a connected non-compact metrizable manifold of dimension
is strongly discrete homogeneous if and only if it has one end (in the
sense of Freudenthal compactification)
On generalized -continua
The notion of -continua was introduced by Alexandroff \cite{ps} as a
generalization of the concept of -manifold. In this note we consider the
cohomological analogue of -continua and prove that any strongly locally
homogeneous, generalized continuum with cohomological dimension is a
generalized -con\-ti\-nuum with respect to the cohomological dimension. In
particular, every strongly locally homogeneous continuum of covering dimension
is a -continuum in the sense of Alexandroff.
An analog of the Mazurkiewicz theorem that no subset of covering dimension
cuts any region of the Euclidean -space is also obtained for
strongly locally homogeneous, generalized continua of cohomological dimension
.Comment: 7 page
Continuous selections of multivalued mappings
This survey covers in our opinion the most important results in the theory of
continuous selections of multivalued mappings (approximately) from 2002 through
2012. It extends and continues our previous such survey which appeared in
Recent Progress in General Topology, II, which was published in 2002. In
comparison, our present survey considers more restricted and specific areas of
mathematics. Note that we do not consider the theory of selectors (i.e.
continuous choices of elements from subsets of topological spaces) since this
topics is covered by another survey in this volume