Atsuji has internally characterized those metric spaces X for which each real-valued continuous function on X is uniformly continuous as follows: (1) the set X' of limit points of X is compact, and (2 ...

Topological groups, which integrate algebraic group structures with continuous topologies, and metric spaces, defined by a distance function, form a fundamental basis for modern mathematical analysis.

This is a preview. Log in through your library . Abstract We give a comparatively simple proof that the complex map $(f, g): T \rightarrow X \times Y$ will be (Borel ...

Three teams of researchers in the US and France have independently developed a new technique to visualize the positions of atoms in real, continuous space, rather than at discrete sites on a lattice.