Pointed space

A dotted topological space is a pair (X, x0 ) consisting of a topological space X and a point x0 in X (basic point, basis point, excellent point). A dotted ( continuous) mapping (X, x0 ) → (Y, y0 ) is a continuous map X → Y that maps x0 to y0.

Often, the basic point is simply denoted by an asterisk.

Is the inclusion of a Kofaserung, then one speaks of a well- dotted space.

Categorical properties

The category of the punctured topological spaces is isomorphic to the comma category. It has zero objects (those spaces which pass a point just out of). Products are the ordinary products of topological spaces, coproducts are single-point associations, ie disjoint unions, in which the respective excellent points are identified with each other, written.

Homotopy classes of punctured pictures

Two dotted pictures

Homotopic to say if it is a continuous map

There. The set of homotopy classes is denoted by dotted pictures.