# Revisiting Variations in Topological Transitivity

## TL;DR

This paper explores different definitions of topological transitivity in dynamical systems, focusing on semiflows, to clarify their relationships and implications within topological dynamics.

## Contribution

It systematically revisits and compares various notions of topological transitivity for semiflows, providing a clearer understanding of their differences and connections.

## Key findings

- Clarified relationships among different transitivity notions
- Identified conditions under which definitions coincide
- Provided insights into semiflow dynamics

## Abstract

Topological dynamical systems $(X,T)$ are actions $T \times X \to X$, given as $(t, x) \to tx$, on a compact, Hausdorff topological space $X$ with $T$ as an acting group or monoid. We take up the property of topological transitivity especially for semiflows $(X,S)$ and discuss the variations in its definitions.