1.1 --- a/src/HOL/Multivariate_Analysis/Topology_Euclidean_Space.thy	Wed Aug 24 15:06:13 2011 -0700
     1.2 +++ b/src/HOL/Multivariate_Analysis/Topology_Euclidean_Space.thy	Wed Aug 24 15:32:40 2011 -0700
     1.3 @@ -7,7 +7,7 @@
     1.4  header {* Elementary topology in Euclidean space. *}
     1.5  
     1.6  theory Topology_Euclidean_Space
     1.7 -imports SEQ Linear_Algebra "~~/src/HOL/Library/Glbs" Norm_Arith
     1.8 +imports SEQ Linear_Algebra "~~/src/HOL/Library/Glbs" Norm_Arith L2_Norm
     1.9  begin
    1.10  
    1.11  (* to be moved elsewhere *)
    1.12 @@ -20,7 +20,7 @@
    1.13    apply(subst(2) euclidean_dist_l2) apply(cases "i<DIM('a)")
    1.14    apply(rule member_le_setL2) by auto
    1.15  
    1.16 -subsection {* General notion of a topologies as values *}
    1.17 +subsection {* General notion of a topology as a value *}
    1.18  
    1.19  definition "istopology L \<longleftrightarrow> L {} \<and> (\<forall>S T. L S \<longrightarrow> L T \<longrightarrow> L (S \<inter> T)) \<and> (\<forall>K. Ball K L \<longrightarrow> L (\<Union> K))"
    1.20  typedef (open) 'a topology = "{L::('a set) \<Rightarrow> bool. istopology L}"