Hybrid algorithm for finding common elements of the set of generalized equilibrium problems and the set of fixed point problems of strictly pseudocontractive mapping.
Hyperbolic homeomorphisms and bishadowing
Hyperbolic homeomorphisms on compact manifolds are shown to have both inverse shadowing and bishadowing properties with respect to a class of δ-methods which are represented by continuous mappings from the manifold into the space of bi-infinite sequences in the manifold with the product topology. Topologically stable homeomorphisms and expanding mappings are also considered.
Hyperconvexity of ℝ-trees
It is shown that for a metric space (M,d) the following are equivalent: (i) M is a complete ℝ-tree; (ii) M is hyperconvex and has unique metric segments.
Hyper-extensions of -algebras
Hyperspace of the approximate inverse limit
Hyperspace retractions for curves [Book]
Hyperspace selections avoiding points
We deal with a hyperspace selection problem in the setting of connected spaces. We present two solutions of this problem illustrating the difference between selections for the nonempty closed sets, and those for the at most two-point sets. In the first case, we obtain a characterisation of compact orderable spaces. In the latter case --- that of selections for at most two-point sets, the same selection property is equivalent to the existence of a ternary relation on the space, known as a cyclic...
Hyperspaces and symmetric products of topological spaces
Hyperspaces of CW-complexes
It is shown that the hyperspace of a connected CW-complex is an absolute retract for stratifiable spaces, where the hyperspace is the space of non-empty compact (connected) sets with the Vietoris topology.
Hyperspaces of Finite Sets in Universal Spaces for Absolute Borel Classes
By Fin(X) (resp. ), we denote the hyperspace of all non-empty finite subsets of X (resp. consisting of at most k points) with the Vietoris topology. Let ℓ₂(τ) be the Hilbert space with weight τ and the linear span of the canonical orthonormal basis of ℓ₂(τ). It is shown that if or E is an absorbing set in ℓ₂(τ) for one of the absolute Borel classes and of weight ≤ τ (α > 0) then Fin(E) and each are homeomorphic to E. More generally, if X is a connected E-manifold then Fin(X) is homeomorphic...
Hyperspaces of infinite-dimensional compacta
Hyperspaces of noncompact metric spaces
Hyperspaces of Peano continua are Hubert cubes
Hyperspaces of Peano continua of euclidean spaces
If X is a space then L(X) denotes the subspace of C(X) consisting of all Peano (sub)continua. We prove that for n ≥ 3 the space is homeomorphic to , where B denotes the pseudo-boundary of the Hilbert cube Q.
Hyperspaces of polyhedra are Hilbert cubes
Hyperspaces of Proximity Spaces.
Hyperspaces of two-dimensional continua
Let X be a compact metric space and let C(X) denote the space of subcontinua of X with the Hausdorff metric. It is proved that every two-dimensional continuum X contains, for every n ≥ 1, a one-dimensional subcontinuum with . This implies that X contains a compact one-dimensional subset T with dim C (T) = ∞.
Hyperspaces of universal curves and 2-cells are true -sets
It is shown that the following hyperspaces, endowed with the Hausdorff metric, are true absolute -sets: (1) ℳ ²₁(X) of Sierpiński universal curves in a locally compact metric space X, provided ℳ ²₁(X) ≠ ∅ ; (2) ℳ ³₁(X) of Menger universal curves in a locally compact metric space X, provided ℳ ³₁(X) ≠ ∅ ; (3) 2-cells in the plane.
Hyperspaces of various locally connected ѕubcontinua
Hyperspaces where convergence to a calm limit implies eventual shape equivalence