Units of continuous functions #
This file concerns itself with
C(X, M)ˣ and
C(X, Mˣ) when
X is a topological space
M has some monoid structure compatible with its topology.
Equivalence between continuous maps into the additive units of an additive monoid with continuous addition and the additive units of the additive monoid of continuous maps.
Equivalence between continuous maps into the units of a monoid with continuous multiplication and the units of the monoid of continuous maps.
Construct a continuous map into the group of units of a normed ring from a function into the normed ring and a proof that every element of the range is a unit.