All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Page 1

Displaying 1 – 19 of 19

Showing per page

Hausdorff topology and uniform convergence topology in spaces of continuous functions

Umberto Artico, Giuliano Marconi (1995)

Commentationes Mathematicae Universitatis Carolinae

The local coincidence of the Hausdorff topology and the uniform convergence topology on the hyperspace consisting of closed graphs of multivalued (or continuous) functions is related to the existence of continuous functions which fail to be uniformly continuous. The problem of the local coincidence of these topologies on C ( X , Y ) is investigated for some classes of spaces: topological groups, zero-dimensional spaces, metric manifolds.

Hereditarily weakly confluent induced mappings are homeomorphisms

Janusz Charatonik, Włodzimierz Charatonik (1998)

Colloquium Mathematicae

For a given mapping f between continua we consider the induced mappings between the corresponding hyperspaces of closed subsets or of subcontinua. It is shown that if either of the two induced mappings is hereditarily weakly confluent (or hereditarily confluent, or hereditarily monotone, or atomic), then f is a homeomorphism, and consequently so are both the induced mappings. Similar results are obtained for mappings between cones over the domain and over the range continua.

Hyperspace selections avoiding points

Valentin Gutev (2022)

Commentationes Mathematicae Universitatis Carolinae

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 of CW-complexes

Bao-Lin Guo, Katsuro Sakai (1993)

Fundamenta Mathematicae

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

Kotaro Mine, Katsuro Sakai, Masato Yaguchi (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

By Fin(X) (resp. F i n k ( X ) ), 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 ℓ ₂ f ( τ ) the linear span of the canonical orthonormal basis of ℓ₂(τ). It is shown that if E = ℓ ₂ f ( τ ) or E is an absorbing set in ℓ₂(τ) for one of the absolute Borel classes α ( τ ) and α ( τ ) of weight ≤ τ (α > 0) then Fin(E) and each F i n k ( E ) are homeomorphic to E. More generally, if X is a connected E-manifold then Fin(X) is homeomorphic...

Hyperspaces of Peano continua of euclidean spaces

Helma Gladdines, Jan van Mill (1993)

Fundamenta Mathematicae

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 L ( ℝ n ) is homeomorphic to B ∞ , where B denotes the pseudo-boundary of the Hilbert cube Q.

Hyperspaces of two-dimensional continua

Michael Levin, Yaki Sternfeld (1996)

Fundamenta Mathematicae

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 T n with d i m C ( T n ) ≥ n . This implies that X contains a compact one-dimensional subset T with dim C (T) = ∞.

Hyperspaces of universal curves and 2-cells are true F σ δ -sets

Paweł Krupski (2002)

Colloquium Mathematicae

It is shown that the following hyperspaces, endowed with the Hausdorff metric, are true absolute F σ δ -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.

Currently displaying 1 – 19 of 19

Page 1