@inproceedings{reinov2017,
author = {Reinov, Oleg and Fahad, Asfand},
title = {On Dentability in Locally Convex Vector Spaces},
year = {2017},
month = {9},
volume = {10},
pages = {14--19},
booktitle = {IJARM Volume 10},
series = {International Journal of Advanced Research in Mathematics},
publisher = {SciPress Ltd},
doi = {10.18052/www.scipress.com/IJARM.10.14},
keywords = {Dentability, Dentable Set, Locally Convex Space},
abstract = {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.}
}