Characterizations of Hilbert Manifolds and Hilbert Cube Manifolds

2020 ◽  
pp. 203-288
Author(s):  
Katsuro Sakai
Keyword(s):  
Hilbert Cube

scholarly journals Characterizing Hilbert cube manifolds by their homological structure

1983 ◽  
Vol 15 (2) ◽  
pp. 197-203
Author(s):  
Terry L. Lay ◽  
John J. Walsh
Keyword(s):  
Hilbert Cube

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

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Hanbiao Yang ◽  
Katsuro Sakai ◽  
Katsuhisa Koshino
Keyword(s):  
Finite Number ◽  
Function Space ◽  
Metrizable Space ◽  
Vietoris Topology ◽  
Hilbert Cube ◽  
Graph Topology ◽  
Closed Sets ◽  
Continuous Map ◽  
Compact Metrizable Space ◽  
Isolated Points

Abstract 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}.

scholarly journals Hilbert cube manifolds

1970 ◽  
Vol 76 (6) ◽  
pp. 1326-1331 ◽  
Author(s):  
T. A. Chapman
Keyword(s):  
Hilbert Cube

scholarly journals Hilbert cube manifolds of maps

1976 ◽  
Vol 6 (1) ◽  
pp. 27-35 ◽  
Author(s):  
Ross Geoghegan
Keyword(s):  
Hilbert Cube
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