Topology

A manifold is like a three-layer cake: on the bottom, a set; in the middle, a topology; on top, an atlas.

Topology is a branch of mathematics.

Algebraic topology is a branch of mathematics.

You are not good in topology. Of course, the south of a globe could be at the top.

1970 [Addison-Wesley], Stephen Willard, General Topology, 2012, Dover, page v, This book is designed to develop the fundamental concepts of general topology which are the basic tools of working mathematicians in a variety of fields.

1974 [Crane, Russak & Co.], H. Graham Flegg, From Geometry to Topology, 2001, Dover, page v, Many university courses in topology plunge immediately into a formalized and entirely abstract presentation of topological concepts.

A set X equipped with a topology #92;tau is called a topological space and denoted (X,#92;tau).

The subsets of a set X which constitute a topology are called the open sets of X.

It is easy to verify that the topology generated by these basic open sets coincides with the definition of the topology on #92;widehat#123;V#125; above, for the Zariski topology and the sheaf of functions #92;operatorname#123;val#125;(f),f regular.