ABSTRACT
Let L t ( X ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003210177/074c5e6c-036b-46e6-9fbd-ef8c3dc19390/content/ieq0078.tif"/> denote the lattice (with respect to ≤) of all topologies on a set X. For T ⊂ L t ( X ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003210177/074c5e6c-036b-46e6-9fbd-ef8c3dc19390/content/ieq0079.tif"/> , VT is the topology generated by ∪T, i.e., the topology whose sets are all unions of finite intersections of sets from topologies in T. From this description it follows that, for each x ∈ X, the collection of all finite intersections ∪ Ui , where Ui is a Ʈi-neighborhood of x (or where Ui comes from a fixed Ʈi-neighborhood base for x) and Ʈi ∈ T for all i, is a V T -neighborhood base at x. One easily sees that ∩T is the infimum.
