Let M be a metric space and let 4>(M) = M be a homeomorphism. 0(m) = X^d^w) is called the orW of m^M under «2> • ■ • (»i<m2...

Recall that a homeomorphism is a continuous bijection with a continuous inverse. Definition 1.1. Let U be a domain in R. Consider vector fields X,Y ∈ X(U) with flows F , F : I × U → U , where I is an open interval in R such that 0 ∈ I. The dynamics of X and Y is said to be C-equivalent if there exists a homeomorphism φ : U → U with the following property: for all t ∈ I there exists a t′ ∈ I suc...

i.e., if every fER attains its maximum modulus on C. As a matter of convenience, we shall, in this paper, abbreviate "maximum modulus algebra on K" to "ilf-algebra." Examples of Af-algebras which come to mind immediately are (a) the algebra ft consisting of all functions which are continuous on K and analytic in U, (b) any subalgebra of ft, (c) any algebra (B which is equivalent to an algebra o...

Topology, or analysis situs, has often been regarded as the study of those properties of point sets (in Euclidean space or in abstract spaces) that are invariant under “homeomorphisms.” Besides the modern concept of homeomorphism, at least three other concepts were used in this context during the late 19th and early 20th centuries, and regarded (by various mathematicians) as characterizing topo...

Crystalline molecular solid solutions are discussed on the basis of homeomorphism and heteromorphism blended molecules.

We study topological queries over two-dimensional spatial databases. First, we show that the topological properties of semialgebraic spatial regions can be completely specified using a classical finite structure, essentially the embedded planar graph of the region boundaries. This provides an invariant characterizing semi-algebraic regions up to homeomorphism. All topological queries on semialg...