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.

Let X be a continuum and let φ:X→X homeomorphism. To construct dynamical system (X,φ) with interesting properties, the often needs to have some complicated topological structure. In this paper, we are interested in one such property: transitivity. By now, various examples of continua been constructed way that is transitive. Mostly, they not path-connected, as pseudo-arc or pseudo-circle, locall...

We give general classification and structure theorems for actions of groups homeomorphisms diffeomorphisms on manifolds, reminiscent classical results (locally) compact groups. This gives a negative answer to Ghys’s extension problem manifolds with boundary, as well all homomorphisms Homeo0(M)→Homeo0(N) when dim(M)=dim(N) (and related diffeomorphisms), complete Homeo0(S1) surfaces. resolves man...

We show that there is no algorithm to decide whether or not a given 4-manifold homeomorphic the connected sum of 12 copies $S^2 \times S^2.