Sr. No | Fine topology | Homeomorphism group | Topological properties |

1 | Zeeman topology (1967): Finest topology which induces three dimensional Euclidean topology on every space-axis and one dimensional Euclidean topology on every time-axis | G = Lorentz group with translations and dilatations | Dossena (2007): neither locally compact nor Lindelof, not normal, separable but not first countable, path-connected but not simply connected |

2 | s-topology: Nanda (1971): Finest topology which induces three dimensional Euclidean topology on every space-like hypersurface | G | G.Agrawal and S. Shrivastava (2012): separable, first countable, path-connected, not regular, not metrizable, not second countable, noncompact, and non-Lindelof, not simply connected |

3 | t-topology: Nanda (1972): Finest topology which induces one dimensional Euclidean topology on every time-like line | G | G.Agrawal and S. Shrivastava (2009): separable, first countable, path-connected, not regular, not metrizable, not second countable, not locally compact, not simply connected |

4 | A-topology: Nanda (1979): Finest topology which induces one dimensional Euclidean topology on every time-like line and light-like line and three dimensional Euclidean topology on every space-like hypersurface | G | G.Agrawal and Soami Pyari Sinha (2014): separable, not first countable, connected and path-connected, not normal, not metrizable, Not comparable with t-topology nor with s-topology |

5 | Fine topologies by Williams (1974): Finest topology which induces one dimensional Euclidean topology on every time-like line and space-like line | Conformal group of Minkowski space whose subgroup is G | Hausdorff, separable, first countable, but not regular and hence not metrizable |

6 | : Finest topology which induces one dimensional Euclidean topology on every straight line | homeomorphisms form projective group generated by full linear group and translations | Weaker than and, Hausdorff, separable and first countable, not regular and hence not metrizable |