steps required to represent the knot as a polygon in the cubic lattice. Several lower bounds for the lattice step numbers of different knots have been obtained by computer simulations but the exact value of the lattice step number seems to be ...
Let X and Z be topological spaces and Y be a subspace of X. A con-
tinuous function f : Y ! Z is extendable to X if there exists a continuous
function f : X ! Z such that f(x) = f(x) for all x 2 Y . If every continuous
function f : Y ! Z is...
In this paper Euclidean and hyperbolic discontinuous isometries* are discussed and compared. The graphic artist M.C. Escher (1898-1972) produced works which have for the structure points, lines, and angles, which repeat in the plane (Euclidean and...