Lattice of Topologies

Abstract

<p> This thesis deals with the lattice of all topologies which may be put on an arbitrary set E. The structure of the lattice is investigated together with its lattice properties. A chapter is included on the co-atoms of the lattice, the ultra-topologies, wherein various topological properties which do and do not hold are investigated. Various topological properties are considered as to which topologies are minimal and maximal such and also which topological properties are preserved under lattice operations and relations.</p>