Homotopy Type Theory pointwise continuous function > history (Rev #3)

Contents

Definition

In premetric spaces

Let TT and VV be types, SS be a TT-premetric space and UU be a VV-premetric space. An function f:SUf:S \to U is continuous at a point c:Sc:S if the limit of ff approaching cc exists and is equal to f(c)f(c)

isContinuousAt(f,c)isContr(lim xcf(x)=f(c))isContinuousAt(f, c) \coloneqq isContr(\lim_{x \to c} f(x) = f(c))

A function ff is pointwise continuous if it is continuous at all points cc:

isPointwiseContinuous(f) c:SisContinuousAt(f,c)isPointwiseContinuous(f) \coloneqq \prod_{c:S} isContinuousAt(f, c)

See also

Revision on March 22, 2022 at 07:59:43 by Anonymous?. See the history of this page for a list of all contributions to it.