Inexistence of Zeeman's fine topology
  The family of topologies that induce the Euclidean metric space on every time axis and every space axis exhibits no maximal element when partially ordered by the relation ``finer than'', as demonstrated in this article. One conclusion and two reflections emerge and are addressed herein:   Conclusion: a. Zeeman's fine topology [1] and G\"{o}bel's extension to arbitrary spacetimes [2] do not exist. Reflections: a. Both authors' attempts may be classified as type-2 strategies, within the taxonomy of [3]. b. How could these inexistent topologies be used for decades? 
Norberto Sainz