LATTICE OF TOPOLOGIES LA'l"rICE OF TOPOLOGIES By

SCOPE AND CON'l'ENTS: This thesis deals v1ith the lattice of all topologies which may be put on an arbitrary set E. 11he structure of the lattice is investigated tor;ether with its lattice properties. A chapter is included on the co-atoms of the lattice, the ultra topoloeies, wherein various topological properties which do and do not hold are inveGtigated. Various topolor;ical properties are considered as to v1hich topologies are minimal and maximal such and also \'1hich topological properties are preserved under lattice operations and relations. (ii) ACKNO':lLEDGMbN'l1S I would. like to express my gratitude to Dr. G. Bruns who consented to be my supervisor and my very great appreciation and gratitude to R. \'/ille without whose guidance and assistance this thesis vmuld never have been. I am most indebted to Dr. Wille v1h