TY - JOUR
T1 - On Dentability in Locally Convex Vector Spaces
AU - Reinov, Oleg
AU - Fahad, Asfand
JF - International Journal of Advanced Research in Mathematics
VL - 10
SP - 14
EP - 19
SN - 2297-6213
PY - 2017
PB - SciPress Ltd
DO - 10.18052/www.scipress.com/IJARM.10.14
UR - https://www.scipress.com/IJARM.10.14
KW - Dentability
KW - Dentable Set
KW - Locally Convex Space
AB - The notions of V-dentability, V-s-dentability and V-f-dentability are introduced. It is shown, in particular, that if B is a bounded sequentially complete convex metrizable subset of a locally convex vector space E and V is a neighborhood of zero in E, then the following are equivalent: 1). B is subset V-dentable; 2). B is subset V-s-dentable; 3). B is subset V-f-dentable. It follows from this that for a wide class of locally convex vector spaces E, which strictly contains the class of (BM) spaces (introduced by Elias Saab in 1978), the following is true: every closed bounded subset of E is dentable if and only if every closed bounded subset of E is f-dentable. Also, we get a positive answer to the Saab's question (1978) of whether the subset dentability and the subset s-dentability are the same forthe bounded complete convex metrizable subsets of any l.c.v. space.
ER -