Abstract
Let C(K) denote the Banach space of all (real or complex) continuous functions on a compact Hausdorff space K.
We present a novel point of view on the classical Arzelà-Ascoli theorem: For every pointwise bounded and equicontinuous subset of C(K) there is a continuous mapping J : β
→ C(K), where β
denotes the Stone-Čech compactification of
, such that
⊂ J (β
); hence the closure of
is compact.
Mathematics Subject Classification (2010):