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Functor of extension in Hilbert cube and Hilbert space

100%

Niemiec P.

Open Mathematics

2014

tom 12

nr 6

887-895

It is shown that if Ω = Q or Ω = ℓ 2, then there exists a functor of extension of maps between Z-sets in Ω to mappings of Ω into itself. This functor transforms homeomorphisms into homeomorphisms, thus giving a functorial setting to a well-known theorem of Anderson [Anderson R.D., On topological infinite deficiency, Michigan Math. J., 1967, 14, 365–383]. It also preserves convergence of sequences of mappings, both pointwise and uniform on compact sets, and supremum distances as well as uniform continuity, Lipschitz property, nonexpansiveness of maps in appropriate metrics.

Topological classification of strong duals to nuclear (LF)-spaces

88%

Banakh T.

Studia Mathematica

2000

tom 138

nr 3

201-208

We show that the strong dual X' to an infinite-dimensional nuclear (LF)-space is homeomorphic to one of the spaces: $ℝ^ω$, $ℝ^∞$, $Q×ℝ^∞$, $ℝ^ω×ℝ^∞$, or $(ℝ^∞)^ω$, where $ℝ^∞ = lim ℝ^n$ and $Q=[-1,1]^ω$. In particular, the Schwartz space D' of distributions is homeomorphic to $(ℝ^∞)^ω$. As a by-product of the proof we deduce that each infinite-dimensional locally convex space which is a direct limit of metrizable compacta is homeomorphic either to $ℝ^∞$ or to $Q×ℝ^∞$. In particular, the strong dual to any metrizable infinite-dimensional Montel space is homeomorphic either to $ℝ^∞$ or to $Q×ℝ^∞$.

Hyperspaces of Peano continua of euclidean spaces

63%

Gladdines H., van Mill J.

Fundamenta Mathematicae

1993

tom 142

nr 2

173-188

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.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Open Mathematics

1 Studia Mathematica

1 Banakh T.

1 Gladdines H.

1 Niemiec P.

1 van Mill J.

1 2014

1 2000

1 1993

Wyniki wyszukiwania

Functor of extension in Hilbert cube and Hilbert space

Topological classification of strong duals to nuclear (LF)-spaces

Hyperspaces of Peano continua of euclidean spaces