Scott W. Williams

A compact F-space not co-absolute with βN−N

Abstract We show that if every Parovicenko space of weight c is co-absolute with β N − N , then c ℵ 1 .

Examples of Recurrence

We present five examples illustrating that results well known for discrete dynamical systems on (locally) compact metric spaces and continuous functions can fail if either (local) compactness or metrizable is removed. Some samples are: A homeomorphism h from the space ℙ of irrationals to itself such that [ℙ; h] has each point recurrent, but [ℙ; h] has no minimal sets. Commuting homeomorphisms f and g from a compact space X to itself such that [X; f] and [X; g] have no common recurrent points.

Paracompactness and products

Abstract We investigate paracompactness in the product of a paracompact space Y with a paracompact linearly ordered topological space X, where certain controls are placed on the subspace ηX of points without a compact neighborhood. If ηX is dispersed, then Xα × Y is paracompact for all finite ordinals α. If the Lindelof degree of Y is less than the least cardinal number, for each nϵeta;X, of any collection of neighborhoods whose intersection does not contain n in its interior, then X ×Y is paracompact.