Approximation Theory
Compactness is a topological property that indicates a space is both closed and bounded. In mathematical analysis, this concept is crucial because it allows for the extension of certain properties from finite sets to infinite sets, such as the ability to extract convergent subsequences from any sequence in the space. Compactness simplifies many problems in approximation theory by ensuring that limits exist and can be approached effectively.
congrats on reading the definition of Compactness. now let's actually learn it.