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Assume that x is of second category and S ⊂ X γ,U).
If X is of second category and S ⊂ X γ,U is pointwise bounded on X, then S ∙ ∈ N X X ).
Assume that x is of second category and Γ ⊂ { f ∈ ℒ γ, U X X, Y ) : f i s c o n t i n u o u s }.
Assume that X is of second category and separable, e.g., separable Fréchet spaces such as L p (0, 1)(p > 0), C[0,1], c0, c, l p (p > 0), etc.
If X is of second category, then the condition "there exists V ∈ N X X ) such that supf∈S,x∈V|f(x)| < +∞" in Corollary 3.20 can be weakened as "there exists V ∈ N X X ) such that sup f∈S |f(x)| < +∞, ∀x ∈ V".
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The examples that Clarke gives of third category properties are magnetism, electrical attractions and gravity.
Besançon-Oyonnax, 187.5km A hilly finale with a rash of third-category climbs in the final 50km means this is hard to predict.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com