منابع مشابه
Dowker Spaces Revisited
In 1951, Dowker proved that a space X is countably paracompact and normal if and only if X×I is normal. A normal space X is called a Dowker space if X × I is not normal. The main thrust of this article is to extend this work with regards α-normality and β-normality. Characterizations are given for when the product of a space X and (ω + 1) is α-normal or β-normal. A new definition, α-countably p...
متن کاملLarge cardinals and Dowker products Chris
We prove that if there is a model of set-theory which contains no first countable, locally compact, scattered, countably paracompact space X, whose Tychonoff square is a Dowker space, then there is an inner model which contains a measurable cardinal.
متن کاملSome Screenable, Σ-relatively Discrete Dowker Spaces
Dowker spaces (that is, normal spaces that are not countably metacompact) are constructed which are also screenable and the countable union of discrete subspaces. The constructions and proofs are easy modifications of the ones for Balogh’s screenable Dowker space [B1]. Balogh’s example is presented alongside the modifications in a new exposition with several new results common to these spaces, ...
متن کاملDowker-type theorems for hyperconvex discs
A hyperconvex disc of radius r is a planar set with nonempty interior that is the intersection of closed circular discs of radius r. A convex disc-polygon of radius r is a set with nonempty interior that is the intersection of a finite number of closed circular discs of radius r. We prove that the maximum area and perimeter of convex disc-n-gons of radius r contained in a hyperconvex disc of ra...
متن کاملLarge Cardinals and Small Dowker Spaces
We prove that, if there is a model of set-theory which contains no first countable, locally compact, scattered Dowker spaces, then there is an inner model which contains a measurable cardinal. A Hausdorff space is normal if, for every pair of disjoint closed sets C and D, there is a pair of disjoint open sets, U containing C and V containing D. A (normal) space is binormal if its product with t...
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ژورنال
عنوان ژورنال: Journal of Applied and Computational Topology
سال: 2019
ISSN: 2367-1726,2367-1734
DOI: 10.1007/s41468-019-00028-9