# Dispersion points and rational curves

## TL;DR

This paper constructs specific connected plane sets with unique properties, embedding them into rational curves, and addresses a question about dispersion points, contributing new examples to the study of rational curves.

## Contribution

It introduces two novel connected plane sets with dispersion points and indecomposability, both embeddable into rational curves, answering a previously open question.

## Key findings

- Constructed a biconnected set with a dispersion point
- Created an indecomposable connected set
- Both sets are completely metrizable

## Abstract

We construct two connected plane sets which can be embedded into rational curves. The first is a biconnected set with a dispersion point. It answers a question of Joachim Grispolakis. The second is indecomposable. Both examples are completely metrizable.