author={A. Lelek},
A topological space is said to be totally paracompact [4] if every open basis contains a locally finite cover. It is known [2] that no reflexive infinite-dimensional Banach space is totally paracompact. It is also known [1], [3] that the space of irrationals with usual topology is not totally paracompact. In the present paper we prove a theorem which gives a necessary condition in order that a subset of a complete metric space be totally paracompact. This allows us to exhibit some pathology… Expand
4 Citations
Base-base paracompactness and subsets of the Sorgenfrey line
A topological space $X$ is called base-base paracompact (John E. Porter) if it has an open base $\mathcal B$ such that every base ${\mathcal B' \subseteq \mathcal B}$ has a locally finite subcoverExpand
Weak infinite-dimensionality in Cartesian products with the Menger Property
Abstract The Menger Property is a classical covering counterpart to σ-compactness. Assuming the Continuum Hypothesis we construct, for each natural n , a separable metrizable space whose n th powerExpand
Dimensional types and P-spaces
We investigate the category of discrete topological spaces, with emphasis on inverse systems of height ω1. Their inverse limits belong to the class of P -spaces, which allows us to exploreExpand
Algorithms for Simultaneous Padé Approximations
We describe how to solve simultaneous Padé approximations over a power series ring K[[x]] for a field K using O~(nω - 1 d) operations in K, where d is the sought precision and $n$ is the number ofExpand


Collections of convex sets which cover a Banach space