Functional Space C (ω), C 0 (ω)
Katuhiko Kanazashi, Hiroyuki Okazaki, Yasunari Shidama (2012)
Formalized Mathematics
Similarity:
In this article, first we give a definition of a functional space which is constructed from all complex-valued continuous functions defined on a compact topological space. We prove that this functional space is a Banach algebra. Next, we give a definition of a function space which is constructed from all complex-valued continuous functions with bounded support. We also prove that this function space is a complex normed space.