Adjacent Topologies

The concepts of immediate predecessor and of immediate successor in the lattice of uniformities and consequently that of adjacent uniformities were introduced by N. Levine and L. Nachman in [3]. In the same paper, the authors have also shown that every uniformity whose topology is not discrete has an immediate successor and that every non trivial uniformity has an immediate predecessor. In this paper we introduce similar concepts of immediate predecessor and immediate successor in the lattice of topologies and consequently that of adjacent topologies. It is then a natural question to ask what types of topologies have immediate predecessors or immediate successors or both. We have attempted to give a solution to this problem. §I deals with immediate successors and §II deals with immediate predecessors. In §III we discuss some properties of adjacent topologies.

公開日:2010年1月24日で登録したコンテンツは、国立情報学研究所において電子化したものです。