diff --git a/dune/gdt/playground/spaces/block.hh b/dune/gdt/playground/spaces/block.hh
index e13c3e68a6f51f58a5a902cef03d8ea89e22658b..b03a661437acdf6ec889d845df92176596de830e 100644
--- a/dune/gdt/playground/spaces/block.hh
+++ b/dune/gdt/playground/spaces/block.hh
@@ -42,7 +42,8 @@ class BlockTraits
 
 public:
   typedef Block<LocalSpaceType> derived_type;
-  static const int polOrder = LocalSpaceType::polOrder;
+  static const int polOrder    = LocalSpaceType::polOrder;
+  static const bool continuous = false;
   typedef typename LocalSpaceType::BackendType BackendType;
   typedef Mapper::Block<LocalSpaceType> MapperType;
   typedef typename LocalSpaceType::BaseFunctionSetType BaseFunctionSetType;
diff --git a/dune/gdt/playground/spaces/cg/fem-localfunctions.hh b/dune/gdt/playground/spaces/cg/fem-localfunctions.hh
index b5b7a3e1b40121aad2bf67488353adf4f552c250..7ad4cce7970ff9d1f1bfcee98a4a268cb881dac4 100644
--- a/dune/gdt/playground/spaces/cg/fem-localfunctions.hh
+++ b/dune/gdt/playground/spaces/cg/fem-localfunctions.hh
@@ -54,7 +54,8 @@ class FemLocalfunctionsBasedTraits
 public:
   typedef GridPartImp GridPartType;
   typedef typename GridPartType::GridViewType GridViewType;
-  static const int polOrder = polynomialOrder;
+  static const int polOrder    = polynomialOrder;
+  static const bool continuous = true;
   static_assert(polOrder >= 1, "Wrong polOrder given!");
 
 private:
diff --git a/dune/gdt/playground/spaces/dg/fem-localfunctions.hh b/dune/gdt/playground/spaces/dg/fem-localfunctions.hh
index b3ab3da606ea86a1e8c4fc216e27454571fec5fb..3c0590ef2e051eedd09be41b16419e86d17b187a 100644
--- a/dune/gdt/playground/spaces/dg/fem-localfunctions.hh
+++ b/dune/gdt/playground/spaces/dg/fem-localfunctions.hh
@@ -57,7 +57,8 @@ class FemLocalfunctionsBasedTraits
 public:
   typedef GridPartImp GridPartType;
   typedef typename GridPartType::GridViewType GridViewType;
-  static const int polOrder = polynomialOrder;
+  static const int polOrder    = polynomialOrder;
+  static const bool continuous = false;
 
 private:
   typedef typename GridPartType::ctype DomainFieldType;
diff --git a/dune/gdt/playground/spaces/dg/fem.hh b/dune/gdt/playground/spaces/dg/fem.hh
index 2209fbf350c2e841b9e7e246aea71b9b3b38d2a3..51d5a7d4a14156a01fa9fbd672fa653fdcea118b 100644
--- a/dune/gdt/playground/spaces/dg/fem.hh
+++ b/dune/gdt/playground/spaces/dg/fem.hh
@@ -50,7 +50,8 @@ public:
   typedef FemBased<GridPartImp, polynomialOrder, RangeFieldImp, rangeDim, rangeDimCols> derived_type;
   typedef GridPartImp GridPartType;
   typedef typename GridPartType::GridViewType GridViewType;
-  static const int polOrder = polynomialOrder;
+  static const int polOrder    = polynomialOrder;
+  static const bool continuous = false;
   static_assert(polOrder >= 1, "Wrong polOrder given!");
 
 private:
diff --git a/dune/gdt/playground/spaces/dg/pdelab.hh b/dune/gdt/playground/spaces/dg/pdelab.hh
index 0fcf24882bdc1f17838f0a24ae9323e54c74fe53..3cbe2861d517f58fb00d4535f3729df21b1dde49 100644
--- a/dune/gdt/playground/spaces/dg/pdelab.hh
+++ b/dune/gdt/playground/spaces/dg/pdelab.hh
@@ -54,7 +54,8 @@ class PdelabBasedTraits
 public:
   typedef PdelabBased<GridViewImp, polynomialOrder, RangeFieldImp, rangeDim, rangeDimCols> derived_type;
   typedef GridViewImp GridViewType;
-  static const int polOrder = polynomialOrder;
+  static const int polOrder    = polynomialOrder;
+  static const bool continuous = false;
 
 private:
   typedef typename GridViewType::ctype DomainFieldType;
diff --git a/dune/gdt/spaces/cg/fem.hh b/dune/gdt/spaces/cg/fem.hh
index 2bc0aed1b04e480d60524cea4f1855eb101a673e..eca8e7db9e957e87acd6c2dc8c1366040989f7ba 100644
--- a/dune/gdt/spaces/cg/fem.hh
+++ b/dune/gdt/spaces/cg/fem.hh
@@ -48,7 +48,8 @@ public:
   typedef FemBased<GridPartImp, polynomialOrder, RangeFieldImp, rangeDim, rangeDimCols> derived_type;
   typedef GridPartImp GridPartType;
   typedef typename GridPartType::GridViewType GridViewType;
-  static const int polOrder = polynomialOrder;
+  static const int polOrder    = polynomialOrder;
+  static const bool continuous = true;
   static_assert(polOrder >= 1, "Wrong polOrder given!");
 
 private:
diff --git a/dune/gdt/spaces/cg/pdelab.hh b/dune/gdt/spaces/cg/pdelab.hh
index 0d831cce66c6b4ca57bc165b2edea8c9eee53d94..27c33812e09d8424b054235cc38c951e8ca49ff2 100644
--- a/dune/gdt/spaces/cg/pdelab.hh
+++ b/dune/gdt/spaces/cg/pdelab.hh
@@ -59,6 +59,7 @@ public:
   typedef GridViewImp GridViewType;
   static const int polOrder = polynomialOrder;
   static_assert(polOrder >= 1, "Wrong polOrder given!");
+  static const bool continuous = true;
 
 private:
   typedef typename GridViewType::ctype DomainFieldType;
diff --git a/dune/gdt/spaces/fv/default.hh b/dune/gdt/spaces/fv/default.hh
index 6e07db332b06040f66873f68575fbf0bbc377a7f..885ade73fb4683ca7cd4cc0fbe4cc9682ec4feef 100644
--- a/dune/gdt/spaces/fv/default.hh
+++ b/dune/gdt/spaces/fv/default.hh
@@ -41,7 +41,8 @@ class DefaultTraits
 {
 public:
   typedef Default<GridViewImp, RangeFieldImp, rangeDim, rangeDimCols> derived_type;
-  static const int polOrder = 0;
+  static const int polOrder    = 0;
+  static const bool continuous = false;
   typedef GridViewImp GridViewType;
   typedef typename GridViewType::IndexSet BackendType;
   typedef typename GridViewType::template Codim<0>::Entity EntityType;
diff --git a/dune/gdt/spaces/interface.hh b/dune/gdt/spaces/interface.hh
index a4a837b18bec7abfd8a9fda65c0d1060d59e43e6..7bd8aaa3a5ab60f6e1644f241b8c375d07f6d0d4 100644
--- a/dune/gdt/spaces/interface.hh
+++ b/dune/gdt/spaces/interface.hh
@@ -79,7 +79,8 @@ class SpaceInterface : public Stuff::CRTPInterface<SpaceInterface<Traits, domain
 {
 public:
   typedef typename Traits::derived_type derived_type;
-  static const int polOrder = Traits::polOrder;
+  static const int polOrder    = Traits::polOrder;
+  static const bool continuous = Traits::continuous;
   typedef typename Traits::BackendType BackendType;
   typedef typename Traits::MapperType MapperType;
   typedef typename Traits::BaseFunctionSetType BaseFunctionSetType;
diff --git a/dune/gdt/spaces/rt/pdelab.hh b/dune/gdt/spaces/rt/pdelab.hh
index 6978ecf0d45bd66f3d1b3abb095043746ab45f7f..1dbba381301ac862bea99e0700cbf71230d3d348 100644
--- a/dune/gdt/spaces/rt/pdelab.hh
+++ b/dune/gdt/spaces/rt/pdelab.hh
@@ -57,7 +57,8 @@ class PdelabBasedTraits
 public:
   typedef PdelabBased<GridViewImp, polynomialOrder, RangeFieldImp, rangeDim, rangeDimCols> derived_type;
   typedef GridViewImp GridViewType;
-  static const int polOrder = polynomialOrder;
+  static const int polOrder    = polynomialOrder;
+  static const bool continuous = false;
   static_assert(polOrder == 0, "Untested!");
   static_assert(rangeDim == GridViewType::dimension, "Untested!");
   static_assert(rangeDimCols == 1, "Untested!");