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Topological Structure of Non-separable Sigma-locally Compact Convex Sets

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Banakh I., Banakh T., Koshino K.

Bulletin of the Polish Academy of Sciences. Mathematics

2013

tom 61

nr 2

149-153

A function space from a compact metrizable space to a dendrite with the hypo-graph topology

100%

Yang H., Sakai K., Koshino K.

Open Mathematics

2015

tom 13

nr 1

Let X be an infinite compact metrizable space having only a finite number of isolated points and Y be a non-degenerate dendrite with a distinguished end point v. For each continuous map ƒ : X → Y , we define the hypo-graph ↓vƒ = ∪ x∈X {x} × [v, ƒ (x)], where [v, ƒ (x)] is the unique arc from v to ƒ (x) in Y . Then we can regard ↓v C(X, Y ) = {↓vƒ | ƒ : X → Y is continuous} as the subspace of the hyperspace Cld(X × Y ) of nonempty closed sets in X × Y endowed with the Vietoris topology. Let [...] be the closure of ↓v C(X, Y ) in Cld(X ×Y ). In this paper, we shall prove that the pair [...] , ↓v C(X, Y )) is homeomorphic to (Q, c0), where Q = Iℕ is the Hilbert cube and c0 = {(xi )i∈ℕ ∈ Q | limi→∞xi = 0}.

Ograniczanie wyników

1 Bulletin of the Polish Academy of Sciences. Mathematics

1 Open Mathematics

2 Koshino K.

1 Banakh I.

1 Banakh T.

1 Sakai K.

1 Yang H.

1 2015

1 2013

Wyniki wyszukiwania

Topological Structure of Non-separable Sigma-locally Compact Convex Sets

A function space from a compact metrizable space to a dendrite with the hypo-graph topology