A new proof of the Banach-stone theorem
1998 ◽
Vol 57
(1)
◽
pp. 55-58
Keyword(s):
Banach's original proof of the Banach-Stone theorem for compact metric spaces uses peak functions, that is, continuous functions which assume their norm in just one point. We show by using nonstandard methods that the peak point approach also works for compact Hausdorff spaces. The peak functions are replaced by internal functions whose standard part is supported in one monad.
2001 ◽
Vol 63
(3)
◽
pp. 475-484
1985 ◽
Vol 101
(3-4)
◽
pp. 203-206
◽
1983 ◽
Vol 26
(1)
◽
pp. 29-48
◽
Keyword(s):
Keyword(s):