On 3/7/2019 7:36 AM, Lawrence Paulson wrote:
In Analysis, we have two equivalent definitions of continuous functions between 
two topological spaces:

lemma "continuous_map X Y f = continuous_on_topo X Y f"
   by (auto simp add: continuous_map_def continuous_on_topo_def vimage_def 
image_def Collect_conj_eq inf_commute)

The first one comes from HOL Light and is defined in Abstract_Topology. The 
latter is declared in Function_Topology.

Obviously we need to eliminate one of them, and I prefer the former name. The 
latter is more logical but clunky, especially when compound with others in 
theorem names.
S├ębastien might have a stronger opinion (I don't), but I would also go for continuous_map: it is in line with open_map, closed_map, quotient_map (which we don't have as constants, but use in theorem names). Moreover, we have more occurrences of continuous_map (174+0 vs 83+39 in isabelle+AFP).

Fabian

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