On thin, very thin, and slim dense sets

On Thin, Very Thin, and Slim Dense Sets

The notions of thin and very thin dense subsets of a product space were introduced by the third author, and in this article we also introduce the notion of a slim dense set in a product. We obtain a number of results concerning the existence and non-existence of these types of small dense sets, and we study the relations among them.

Thin-Type Dense Sets and Related Properties

We build on Gruenhage, Natkaniec, and Piotrowski’s study of thin, very thin, and slim dense sets in products, and the related notions of (NC) and (GC) which they introduced. We find examples of separable spaces X such that X has a thin or slim dense set but no countable one. We characterize ordered spaces that satisfy (GC) and (NC), and we give an example of a separable space which satisfies (G...

Thin clients: slim security?

ENLARGED FUNDAMENTALLY VERY THIN Hv-STRUCTURES

We study a new class of $H_v$-structures called Fundamentally Very Thin. This is an extension of the well known class of the Very Thin hyperstructures. We present applications of these hyperstructures.

enlarged fundamentally very thin hv-structures

we study a new class of $h_v$-structures called fundamentally very thin. this is an extension of the well known class of the very thin hyperstructures. we present applications of these hyperstructures.