Algebraic Separation and Shadowing of Arbitrary Sets

Jerzy Grzybowski, Diethard Pallaschke, and Ryszard Urbański. "Algebraic Separation and Shadowing of Arbitrary Sets." Commentationes Mathematicae 53.2 (2013): null. <http://eudml.org/doc/292441>.

@article{JerzyGrzybowski2013,
abstract = {In this paper we consider a generalization of the separation technique proposed in [10,4,7] for the separation of finitely many compact convex sets $A_i,~i \in I $ by another compact convex set $S$ in a locally convex vector space to arbitrary sets in real vector spaces. Then we investigate the notation of shadowing set which is a generalization of the notion of separating set and construct separating sets by means of a generalized Demyanov-difference in locally convex vector spaces.},
author = {Jerzy Grzybowski, Diethard Pallaschke, Ryszard Urbański},
journal = {Commentationes Mathematicae},
keywords = {separation, geometry of convex sets, Demyanov difference, data-classification},
language = {eng},
number = {2},
pages = {null},
title = {Algebraic Separation and Shadowing of Arbitrary Sets},
url = {http://eudml.org/doc/292441},
volume = {53},
year = {2013},
}

TY - JOUR
AU - Jerzy Grzybowski
AU - Diethard Pallaschke
AU - Ryszard Urbański
TI - Algebraic Separation and Shadowing of Arbitrary Sets
JO - Commentationes Mathematicae
PY - 2013
VL - 53
IS - 2
SP - null
AB - In this paper we consider a generalization of the separation technique proposed in [10,4,7] for the separation of finitely many compact convex sets $A_i,~i \in I $ by another compact convex set $S$ in a locally convex vector space to arbitrary sets in real vector spaces. Then we investigate the notation of shadowing set which is a generalization of the notion of separating set and construct separating sets by means of a generalized Demyanov-difference in locally convex vector spaces.
LA - eng
KW - separation, geometry of convex sets, Demyanov difference, data-classification
UR - http://eudml.org/doc/292441
ER -