regular map

Definitions

1. 1

   A morphism between algebraic varieties.

   • We now find out how a regular map acts on the ring of regular functions on a closed set.[…]Moreover, regular maps can be characterised as the maps that take regular functions into regular functions.
   • Since one expects that the canonical projection f#58;X#92;rightarrowX#47;G is a regular map of algebraic varieties and so has closed fibres, all orbits must be closed subsets in the Zariski topology of X.
2. 2

   A symmetric tessellation of a closed surface

   A symmetric tessellation of a closed surface; a decomposition of a two-dimensional manifold into topological disks such that every flag (incident vertex-edge-face triple) can be transformed into any other flag by a symmetry (i.e., an automorphism) of the decomposition.

   • If n is finite, the regular map is a tessellation of the plane by congruent n-sided polygons, m of which meet at each vertex.

The neighborhood