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.
@article{bwmeta1.element.doi-10_2478_v10037-012-0003-3,
author = {Katuhiko Kanazashi and Hiroyuki Okazaki and Yasunari Shidama},
title = {
Functional Space
C
($\omega$),
C
0
($\omega$)
},
journal = {Formalized Mathematics},
volume = {20},
year = {2012},
pages = {15-22},
zbl = {1276.60032},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-012-0003-3}
}
Katuhiko Kanazashi; Hiroyuki Okazaki; Yasunari Shidama.
Functional Space
C
(ω),
C
0
(ω)
. Formalized Mathematics, Tome 20 (2012) pp. 15-22. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-012-0003-3/
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