regular map

Noun

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. - 1994, Igor R....
   • 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. - 2003, Igor...
   • 2017, José F. Fernando, José M. Gamboa, Carlos Ueno, Polynomial, regular and Nash images of Euclidean spaces, Fabrizio Broglia, Françoise Delon, Max Dickmann, Danielle Gondard-Cozette, Victoria Ann Powers (editors),...
2. 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.
   • 1990 [McGraw-Hill], Jay Kappraff, Connections: The Geometric Bridge Between Art and Science, 2001, World Scientific, page 141, Just as there are only five regular maps on the sphere (or plane), there are only three...
   • 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. - 2010, Jozef Širáñ, Yan Wang, “Maps with highest level of symmetry that are even more...
   • If M is a regular map of type #92;#123;p,q#92;#125;, then #92;mathit#123;Aut#125;(M)#92;approx#92;Delta(p,q,2)#47;N for some normal subgroup N#92;#92;trianglelefteq#92;#92;Delta(p,q,2). Similar statements hold for the...