Here we are going to consider problems of the following type:
We have a family set F of satisfying certain conditions, meaning that we can choose a bounded number of points such that each set of F contains at least one of them.
Technically, $\epsilon$-nets have widely application among mathematics and computer science. for more information see below links ;
https://scs.carleton.ca/content/vc-dimension-and-epsilon-nets-applications-visibility-problems
Weather you are famillier with prelimenary defination or not I provided some references here:
Chapter 10: LECTURES ON DISCRETE GEOMETRY (Jiri Matousek) http://www.ti.inf.ethz.ch/ew/lehre/CG12/lecture/Chapter%2015.pdf http://sarielhp.org/teach/08/a/lec/24_vcdim.pdf https://www.cs.ucsb.edu/~suri/cs235/VcDimension.pdf
The Basic is simple for who is interested in combinatorics problem... But difficulties come to you from initiate
Some one tell me what is the general definition $\epsilon$- net theorems ??? I've found 3 difference version of them :
First
Chapter 10: LECTURES ON DISCRETE GEOMETRY (Jiri Matousek)
Second
http://sarielhp.org/teach/08/a/lec/24_vcdim.pdf
Third
https://www.cs.ucsb.edu/~suri/cs235/VcDimension.pdf
I want categorize them in order to use in my Bachelor Project So even intoducing a new reference or new application or a new combinatorial approach will help me alot...