Contents

1. Introduction

2. Semi topology

3. Transitive sets and topens

4. Open interiors, communities, and regular points

5. Closed sets

6. (Un)conflicted points: transitivity of ≬

7. The product semi topology

8. Computing semi topologies: witnessed sets and the witness semi topology

9. (Strongly) chain-complete semi topologies

10. Kernels: the atoms in a community

11. Dense subsets and continuous extensions

12. Conclusions