*Modern differential geometry for physicists*. I guess the first question would be what you guys think of this book, does it cover all the necessary stuff (it's my preparation for general relativity)? Sadly I'm already having trouble with the introductory chapter on topology.. I'll post my questions in this topic.

Isham starts out by defining filters and neighbourhood structures on a set X. A topological space is then a special kind of neighbourhood space. The proof of the following theorem is left up to the reader, but this reader needs some pointers..

"A neighbourhood space (X,N) is a topological space if and only if each filter N(x) has a filter base consisting of open sets."

When a filter base consists of open sets, what consequences does that have for the filter it generates?