Homotopy Type Theory
pointwise continuous function > history (Rev #10)
Contents
Definition
In rational numbers
Let be the rational numbers. An function is continuous at a point
is pointwise continuous in if it is continuous at all points :
is uniformly continuous in if
In Archimedean ordered fields
Let be an Archimedean ordered field. An function is continuous at a point
is pointwise continuous in if it is continuous at all points :
is uniformly continuous in if
Most general definition
Let be a type with a predicate between the type of all nets in
and itself, and let be a type with a predicate between the type of all nets in
and itself.
A function is continuous at a point
is pointwise continuous if it is continuous at all points :
See also
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