chapter  6
25 Pages

Transitive Spaces

WithFletcher Peter, William F. Lindgren

In the previous chapters we considered uniform spaces only to establish results that pertain to a wider class of quasi-uniformities, and in general, throughout this text we give the uniform spaces short shrift because an equitable allotment of time to them would prove overwhelming. Even when we restrict our attention to transitive quasi-uniformities the study of the uniformities among them leads from our province into such topics as dimension theory, valuation rings, and Boolean algebras. In this section, therefore, we only consider transitive uniformities in order to obtain insight into unresolved problems concerning transitive quasi-uniformities.