If is the causal completion of an open set U, then is an isomorphism (primitive causality).

In topology, a set U is called an open set if it does not contain any of its boundary points.

In mathematics, a Grothendieck universe is a set U with the following properties:

For every open set U in S, the identity map on U is in Γ.

Then for each set, choose an open set U containing x that doesn't intersect it.

But removing the open set U would render χ discontinuous.

For each point x in an open set U, there is a base element containing x and contained in U.

A partial fix for this problem can be found if we agree to restrict our attention to subsets of a fixed set U called the universe.

An analytic function in an open set U is called a function element.

On an open set U as before, a section of is the product of a holomorphic function s with the form df/f.