Abstract
AbstractFor a given closed nonempty subset E of a Hilbert space H, the singular set $$\Sigma _E$$
Σ
E
consists of the points in $$H\setminus E$$
H
\
E
where the distance function $$d_E$$
d
E
is not Fréchet differentiable. It is known that $$\Sigma _E$$
Σ
E
is a weak deformation retract of the open set $$\mathcal {G}_E=\{x\in H: d_{\overline{{\text {co}}}\,E}(x)< d_E(x)\}$$
G
E
=
{
x
∈
H
:
d
co
¯
E
(
x
)
<
d
E
(
x
)
}
. This short paper sheds light on the relationship between the connected components of the three sets $$\Sigma _E\subset \mathcal {G}_E\subseteq H{\setminus } E$$
Σ
E
⊂
G
E
⊆
H
\
E
.
Funder
Lulea University of Technology
Publisher
Springer Science and Business Media LLC
Reference18 articles.
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