A classification of continua by certain cutting properties
A classification of dynamical systems
A classification of H-closed extensions
A classification of inverse limit spaces of tent maps with periodic critical points
We work within the one-parameter family of symmetric tent maps, where the slope is the parameter. Given two such tent maps , with periodic critical points, we show that the inverse limit spaces and are not homeomorphic when a ≠ b. To obtain our result, we define topological substructures of a composant, called “wrapping points” and “gaps”, and identify properties of these substructures preserved under a homeomorphism.
A classification of ordinals up to Borel isomorphism
We consider the Borel structures on ordinals generated by their order topologies and provide a complete classification of all ordinals up to Borel isomorphism in ZFC. We also consider the same classification problem in the context of AD and give a partial answer for ordinals ≤ω₂.
A classification of separable Rosenthal compacta and its applications [Book]
A Classification Of Topological Spaces. Z-Number Of Spaces
A classification of triangular maps of the square.
A classification scheme for axioms weaker than
A closed separable subspace not being a retract of
A coarse convergence group need not be precompact
A coding of separable Banach spaces. Analytic and coanalytic families of Banach spaces
When the set of closed subspaces of C(Δ), where Δ is the Cantor set, is equipped with the standard Effros-Borel structure, the graph of the basic relations between Banach spaces (isomorphism, being isomorphic to a subspace, quotient, direct sum,...) is analytic non-Borel. Many natural families of Banach spaces (such as reflexive spaces, spaces not containing ℓ₁(ω),...) are coanalytic non-Borel. Some natural ranks (rank of embedding, Szlenk indices) are shown to be coanalytic ranks. Applications...
A cohomological index of Fuller type for parameterized set-valued maps in normed spaces
We construct a cohomological index of the Fuller type for set-valued flows in normed linear spaces satisfying the properties of existence, excision, additivity, homotopy and topological invariance. In particular, the constructed index detects periodic orbits and stationary points of set-valued dynamical systems, i.e., those generated by differential inclusions. The basic methods to calculate the index are also presented.
A collection of dendroids.
A combinatorial proof of the extension property for partial isometries
We present a short and self-contained proof of the extension property for partial isometries of the class of all finite metric spaces.
A common end point theorem for set-valued generalized -weak contraction.
A common fixed point theorem
A common fixed point theorem
A common fixed point theorem for commuting expanding maps on nilmanifolds.
A common fixed point theorem for compatible mappings on a normed vector space.