Quasicontinuous selections for compact-valued multifunctions
Quasi-equivalence of compacta and spaces of components.
Let X, Y be two compacta with Sh(X) = Sh (Y). Then, the spaces of components of X, Y are homeomorphic. This does not happen, in general, when X, Y are quasi-equivalent. In this paper we give a sufficient condition for the existence of a homeomorphism between the spaces of components of two quasi-equivalent compacta X, Y which maps each component in a quasi-equivalent component.
Quasi-monotone and confluent images of irreducible continua
Quasi-nonexpansive multi-valued maps and selections
Quasi-pseudometrizability of the point open ordered spaces and the compact open ordered spaces.
(Quasi)-uniformities on the set of bounded maps.
Quelques remarques sur la quasi-continuité des multifonctions
Questions
Quotient spaces defined by linear relations
Quotients of peripherally continuous functions
We characterize the family of quotients of peripherally continuous functions. Moreover, we study cardinal invariants related to quotients in the case of peripherally continuous functions and the complement of this family.
-continuous functions.
-compact spaces and -connected spaces.
-supercontinuous functions
A new class of functions called “-supercontinuous functions” is introduced. Their basic properties are studied and their place in the hierarchy of strong variants of continuity that already exist in the literature is elaborated. The class of -supercontinuous functions properly includes the class of -supercontinuous functions, Tyagi, Kohli, Singh (2013), which in its turn contains the class of -supercontinuous ( clopen continuous) functions, Singh (2007), Reilly, Vamanamurthy (1983), and is...
Raising dimension under all projections
As a special case of the general question - “What information can be obtained about the dimension of a subset of by looking at its orthogonal projections into hyperplanes?” - we construct a Cantor set in each of whose projections into 2-planes is 1-dimensional. We also consider projections of Cantor sets in whose images contain open sets, expanding on a result of Borsuk.
Ramsey, Lebesgue, and Marczewski sets and the Baire property
We investigate the completely Ramsey, Lebesgue, and Marczewski σ-algebras and their relations to the Baire property in the Ellentuck and density topologies. Two theorems concerning the Marczewski σ-algebra (s) are presented. THEOREM. In the density topology D, (s) coincides with the σ-algebra of Lebesgue measurable sets. THEOREM. In the Ellentuck topology on , is a proper subset of the hereditary ideal associated with (s). We construct an example in the Ellentuck topology of a set which is...
Ramsey theory for structures: Nešetřil's result on finite metric spaces.
Ramsey-like properties for bi-Lipschitz mappings of finite metric spaces
Let , be metric spaces and an injective mapping. We put ; , , and (the distortion of the mapping ). Some Ramsey-type questions for mappings of finite metric spaces with bounded distortion are studied; e.g., the following theorem is proved: Let be a finite metric space, and let , be given numbers. Then there exists a finite metric space , such that for every mapping ( arbitrary metric space) with one can find a mapping , such that both the mappings and have distortion at...
Random differential inclusions: Measurable selection approach
Random theorems in topology
Range closure extension of input-output relations of topological general systems