Reference
  ~~~~~~~~~

  Johnstone, P.T., Linton, F.E.J. and Paré, R., 
  Injectives in Topoi, II: Connections with the
  Axiom of Choice. In: Categorical Topology,
  Proceedings, Berlin, 1978; Springer LNM 719, 
  1979, pp. 207-216.  

  One of the results here used a Baire Category argument to explain why a certain double covering of what’s known as Heath’s V-space – the (non-discrete) result of pasting a (closed) discrete x-axis to an (open) discrete upper half-plane – admits no continuous section. Today I’ll give a more basic explanation for that phenomenon.