Entourages. Asymmetric Uniformity

Abstract

The uniform structure as discussed in chapters VIII and X is an extension of the classical one introduced by Tukey ([259]) in 1940. This was, however, not the first approach to modeling uniform phenomena as known from metric spaces. It was preceded by the Weil uniformities ([272], 1938) based on distinguished neighbourhoods of the diagonal of the space in question, the so-called entourages. In fact in the first decades the topologists preferred the Weil model and it took until 1964 when the cover approach was brought to the focus of interest by the celebrated Isbell’s monograph [135].