Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Descriptive Proximities I: Properties and interplay between classical
  proximities and overlap   The theory of descriptive nearness is usually adopted when dealing with sets
that share some common properties even when the sets are not spatially close,
i.e., the sets have no members in common. Set description results from the use
of probe functions to define feature vectors that describe a set and the
nearness of sets is given by their proximities. A probe on a non-empty set $X$
is a real-valued function $\Phi: X \rightarrow \mathbb{R}^n$, where $\Phi(x)=
(\phi_1(x),.., \phi_n(x))$. We establish a connection between relations on an
object space $X$ and relations on the feature space $\Phi(X).$ Having as
starting point the Peters proximity, two sets are \emph{descriptively near}, if
and only if their descriptions intersect. In this paper, we construct a
theoretical approach to a more visual form of proximity, namely, descriptive
proximity, which has a broad spectrum of applications. We organize descriptive
proximities on two different levels: weaker or stronger than the Peters
proximity. We analyze the properties and interplay between descriptions on one
side and classical proximities and overlap relations on the other side.

24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio