At its core, continuity implies that small changes in the input of a function result in small changes in its output. More ...

A table of values presents a discrete snapshot of a function's behavior. It lists specific x -values and their corresponding ...

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 ...

We extend lemmas by Bourgain-Brezis-Mironescu (2001), and Maz'ya-Shaposhnikova (2002), on limits of Sobolev spaces, to the setting of interpolation scales. This is achieved by means of establishing ...