  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?
