Meaning of regular map | Babel Free

Definitions

1. A morphism between algebraic varieties.
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.

Examples

“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.”

“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), Ordered Algebraic Structures and Related Topics: International Conference, American Mathematical Society, page 160, The 1-dimensional semialgebraic set 𝒮:=x>0,xy=1 is the image of the regular map f: R ²→ R ²,(x,y)↦((xy-1)²+x²,1/((xy-1)²+x²)).”

“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 classes of regular maps that can be created on a torus.”

“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.”

“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 class of orientably regular maps and subgroups of #92;Delta#43; and #92;Delta#43;(p,q,2).”

CEFR level