Approximations of Symmetry

A (sub)base B https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203741443/6e3a22fd-c16c-4032-8a63-4328d52b721d/content/eq67.tif"/> for a quasi-uniformity is transitive provided that each B ε B https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203741443/6e3a22fd-c16c-4032-8a63-4328d52b721d/content/eq68.tif"/> is a transitive relation. A quasi-uniformity with a transitive (sub)base is called a transitive quasi-uniformity.