A Survey on Wallman Bases

Abstract

Wallman bases are frequently used in compactification processes of topological spaces. However, they are also related with quasi–uniform structures and they are useful to characterize some topological properties. We present a brief survey on the subject which supports these statements.

Keywords

• Wallman basis
• Annular basis
• Ultrafilter
• Perfect extension
• Wallman type
• Regular Wallman
• Equivalent compactifications
• Cover uniformity basis
• Quasi–uniformity Transitive
• Totally bounded
• Symmetric
• Point symmetric
• Locally symmetric