publication . Article . 2002

Constructing Type I nonmetrisable manifolds with given ϒ-trees☆

Greenwood, Sina;
Open Access
  • Published: 01 Aug 2002 Journal: Topology and its Applications, volume 123, issue 1, pages 91-101 (issn: 0166-8641, Copyright policy)
  • Publisher: Elsevier BV
Abstract Nyikos has defined a tree, denoted ϒ , associated with any given Type I nonmetrisable manifold. In this paper, given an arbitrary well-pruned ω 1 -tree, T , we construct a Type I manifold such that its ϒ -tree is T . We show that whenever a Type I manifold contains a copy of ω 1 , its ϒ -tree must contain an uncountable branch. We address the problem of whether or not an arbitrary tree admits a Type I manifold which is ω 1 -compact.
free text keywords: Geometry and Topology, Type I manifold, ϒ-tree, ω1-compact, Copy of ω1
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