# On generating regular Cantorvals connected with geometric Cantor sets

## TL;DR

This paper investigates the properties of regular Cantorvals linked with geometric Cantor sets, demonstrating they are not achievement sets of any series but can be attractors of affine IFS.

## Contribution

It establishes that certain Cantorvals cannot be achievement sets but can be generated as attractors of affine iterated function systems.

## Key findings

- Cantorvals linked with geometric Cantor sets are not achievement sets.
- Many such Cantorvals are attractors of affine IFS.
- Provides insight into the structure and generation of Cantorvals.

## Abstract

We show that the Cantorvals connected with the geometric Cantor sets are not achievement sets of any series. However many of them are attractors of IFS consisting of affine functions.