• Publications
  • Influence
Topological Properties of Manifolds
In this chapter we investigate the consequences for a manifold, when certain topological properties are assumed. In particular, we develop an important analytical tool, called partition of unity. 5.1Expand
  • 16
  • 1
  • PDF
Non-metrisable Manifolds
Topological Manifolds.- Edge of the World: When are Manifolds Metrisable?.- Geometric Tools.- Type I Manifolds and the Bagpipe Theorem.- Homeomorphisms and Dynamics on Non-Metrisable Manifolds.- AreExpand
  • 7
  • 1
Spaces with property pp
Abstract This paper continues the study of pp spaces. It is shown that under a wide variety of circumstances, pp spaces are paracompact. However, examples of pp non-paracompact spaces are given, someExpand
  • 2
  • 1
Metrisability of Manifolds
Manifolds have uses throughout and beyond Mathematics and it is not surprising that topologists have expended a huge effort in trying to understand them. In this article we are particularlyExpand
  • 10
  • 1
  • PDF
Did the Young Volterra Know About Cantor
In [3], Dunham recalls Volterra's proof [5] that any two functions from DR to itself that are continuous on dense subsets of DR have a common point of continuity. The only use of the completenessExpand
  • 5
  • 1
A strongly hereditarily separable, nonmetrisable manifold
Abstract Assuming the Continuum Hypothesis, a nonmetrisable manifold is constructed, all of whose finite powers are hereditarily separable.
  • 6
  • 1
Enriched lattice-valued convergence groups
We present the category SL-GConvGrp, of stratified L-generalized convergence groups, and some of its subcategories. Expand
  • 4
In this paper, we focus on enriched cl-premonoid-valued topological groups, and their so-called change-of-basis lattice. In so doing, we take L as an enriched cl-premonoid and present a categoryExpand
  • 3
Homogeneous and inhomogeneous manifolds
All metaLindelof, and most countably paracompact, homogeneous manifolds are Hausdorff. Metacompact manifolds are never rigid. Every countable group can be realized as the group of autohomeomorphismsExpand
  • 3
  • PDF