On CE-images of the Hubert cube and characterization of Q-manifolds

Toruńczyk, H.

doi:10.4064/fm-106-1-31-40

Cited by 165 publications

(60 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…‫ގ‬ is a compact Hilbert cube manifold [Edwards 1980], or equivalently, a compact ANR with the disjoint-cells property [Toruńczyk 1980]. Choose a map f :X → [0, 1] with f −1 ({0}) = Z and define g : ‫ގ‬ .…”

Section: Coxeter Group Boundariesmentioning

confidence: 99%

On the fundamental groups of trees of manifolds

Fischer¹,

Guilbault²

2005

Pacific J. Math.

View full text Add to dashboard Cite

Section: Coxeter Group Boundariesmentioning

confidence: 99%

On the fundamental groups of trees of manifolds

Fischer¹,

Guilbault²

2005

Pacific J. Math.

View full text Add to dashboard Cite

“…The disjoint disks property of J. W. Cannon is crucial in the current characterizations of finite dimensional manifolds [Ca, Ed, Qu] as are the disjoint and discrete cells properties of H. Torunczyk in the current characterizations of infinite dimensional manifolds modeled on the Hubert cube and Hubert space [Toi,T02]. It was during an investigation of factors of Hubert space manifolds that the author was led to examine the various general position properties that the finite products of dendrites and special subsets of dendrites possess.…”

Section: Introductionmentioning

confidence: 99%

General Position Properties Satisfied by Finite Products of Dendrites

Bowers¹

1985

Transactions of the American Mathematical Society

View full text Add to dashboard Cite

ABSTRACT. Let Ä be a dendrite whose endpoints are dense and let A be the complement in A of a dense er-compact collection of endpoints of A. This paper investigates various general position properties that finite products of A and A possess. In particular, it is shown that (i) if X is an LCn-space that satisfies the disjoint n-cells property, then X X A satisfies the disjoint (n + l)-cells property, (ii) An X [-1,1] is a compact (n + l)-dimensional AR that satisfies the disjoint n-cells property, (iii) Än+1 is a compact (n + l)-dimensional AR that satisfies the stronger general position property that maps of n-dimensional compacta into Än+1 are approximable by both Z-raaps and Zn -embeddings, and (iv) An+1 is a topologically complete (n + l)-dimensional AR that satisfies the discrete n-cells property and as such, maps from topologically complete separable n-dimensional spaces into An+1 are strongly approximable by closed Zn-embeddings.

show abstract

“…Hence C π (I ×I) has the disjoint n-cell property for each n, so by Toruńczyk's characterization theorem [14], C π (I × I) is homeomorphic to Q. S t e p 3. p * n,n+1 : C π (I n+1 × I n+1 ) → C π (I n × I n ) is a cell-like map.…”

mentioning

confidence: 99%

On a compactification of the homeomorphism group of the pseudo-arc

Kawamura

1991

Colloq. Math.

View full text Add to dashboard Cite

On CE-images of the Hubert cube and characterization of Q-manifolds

Cited by 165 publications

References 0 publications

On the fundamental groups of trees of manifolds

On the fundamental groups of trees of manifolds

General Position Properties Satisfied by Finite Products of Dendrites

On a compactification of the homeomorphism group of the pseudo-arc

Contact Info

Product

Resources

About