About: Half-disk topology

In mathematics, and particularly general topology, the half-disk topology is an example of a topology given to the set , given by all points in the plane such that . The set can be termed the closed upper half plane. To give the set a topology means to say which subsets of are "open", and to do so in a way that the following axioms are met: 1. * The union of open sets is an open set. 2. * The finite intersection of open sets is an open set. 3. * The set and the empty set are open sets.