Author:
Derȩgowska Beata,Gryszka Beata,Gryszka Karol,Wójcik Paweł
Abstract
AbstractThe investigations of the smooth points in the spaces of continuous function were started by Banach in 1932 considering function space $$\mathcal {C}(\Omega )$$
C
(
Ω
)
. Singer and Sundaresan extended the result of Banach to the space of vector valued continuous functions $$\mathcal {C}(\mathcal {T},E)$$
C
(
T
,
E
)
, where $$\mathcal {T}$$
T
is a compact metric space. The aim of this paper is to present a description of semi-smooth points in spaces of continuous functions $$\mathcal {C}_0(\mathcal {T},E)$$
C
0
(
T
,
E
)
(instead of smooth points). Moreover, we also find necessary and sufficient condition for semi-smoothness in the general case.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Mathematics (miscellaneous)
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