diff -r 18da2a87421c -r 5e4a1664106e src/HOL/Limits.thy --- a/src/HOL/Limits.thy Sun Aug 14 10:25:43 2011 -0700 +++ b/src/HOL/Limits.thy Sun Aug 14 10:47:47 2011 -0700 @@ -283,10 +283,10 @@ definition within :: "'a filter \ 'a set \ 'a filter" (infixr "within" 70) where "F within S = Abs_filter (\P. eventually (\x. x \ S \ P x) F)" -definition nhds :: "'a::topological_space \ 'a filter" +definition (in topological_space) nhds :: "'a \ 'a filter" where "nhds a = Abs_filter (\P. \S. open S \ a \ S \ (\x\S. P x))" -definition at :: "'a::topological_space \ 'a filter" +definition (in topological_space) at :: "'a \ 'a filter" where "at a = nhds a within - {a}" lemma eventually_within: @@ -517,8 +517,8 @@ subsection {* Limits *} -definition tendsto :: "('a \ 'b::topological_space) \ 'b \ 'a filter \ bool" - (infixr "--->" 55) where +definition (in topological_space) + tendsto :: "('b \ 'a) \ 'a \ 'b filter \ bool" (infixr "--->" 55) where "(f ---> l) F \ (\S. open S \ l \ S \ eventually (\x. f x \ S) F)" ML {*