diff --git a/include/boost/geometry/core/closure.hpp b/include/boost/geometry/core/closure.hpp
index 9792e463e..d3ac5a9df 100644
--- a/include/boost/geometry/core/closure.hpp
+++ b/include/boost/geometry/core/closure.hpp
@@ -45,6 +45,26 @@ struct closure
 } // namespace traits
 
 
+#ifndef DOXYGEN_NO_DETAIL
+namespace core_detail { namespace closure
+{
+
+struct closed
+{
+    static const closure_selector value = geometry::closed;
+};
+
+struct open
+{
+    static const closure_selector value = geometry::open;
+};
+
+
+}} // namespace detail::point_order
+#endif // DOXYGEN_NO_DETAIL
+
+
+
 #ifndef DOXYGEN_NO_DISPATCH
 namespace core_dispatch
 {
@@ -59,6 +79,18 @@ struct closure
         );
 };
 
+template <typename Box>
+struct closure<point_tag, Box> : public core_detail::closure::open {};
+
+template <typename Box>
+struct closure<box_tag, Box> : public core_detail::closure::closed {};
+
+template <typename Box>
+struct closure<segment_tag, Box> : public core_detail::closure::open {};
+
+template <typename LineString>
+struct closure<linestring_tag, LineString> : public core_detail::closure::open {};
+
 
 template <typename Ring>
 struct closure<ring_tag, Ring>
diff --git a/include/boost/geometry/multi/algorithms/intersection.hpp b/include/boost/geometry/multi/algorithms/intersection.hpp
index 612722cfd..3bc16e353 100644
--- a/include/boost/geometry/multi/algorithms/intersection.hpp
+++ b/include/boost/geometry/multi/algorithms/intersection.hpp
@@ -10,6 +10,7 @@
 
 
 #include <boost/geometry/algorithms/intersection.hpp>
+#include <boost/geometry/multi/core/closure.hpp>
 #include <boost/geometry/multi/core/geometry_id.hpp>
 #include <boost/geometry/multi/core/is_areal.hpp>
 #include <boost/geometry/multi/core/point_order.hpp>
diff --git a/include/boost/geometry/multi/algorithms/union.hpp b/include/boost/geometry/multi/algorithms/union.hpp
index 73ae2e04a..c416a7519 100644
--- a/include/boost/geometry/multi/algorithms/union.hpp
+++ b/include/boost/geometry/multi/algorithms/union.hpp
@@ -10,6 +10,7 @@
 
 
 #include <boost/geometry/algorithms/union.hpp>
+#include <boost/geometry/multi/core/closure.hpp>
 #include <boost/geometry/multi/core/geometry_id.hpp>
 #include <boost/geometry/multi/core/is_areal.hpp>
 #include <boost/geometry/multi/core/point_order.hpp>
diff --git a/include/boost/geometry/multi/algorithms/within.hpp b/include/boost/geometry/multi/algorithms/within.hpp
index b038f9f46..ac0324163 100644
--- a/include/boost/geometry/multi/algorithms/within.hpp
+++ b/include/boost/geometry/multi/algorithms/within.hpp
@@ -13,6 +13,8 @@
 #include <boost/range.hpp>
 
 #include <boost/geometry/algorithms/within.hpp>
+#include <boost/geometry/multi/core/closure.hpp>
+#include <boost/geometry/multi/core/point_order.hpp>
 #include <boost/geometry/multi/core/tags.hpp>
 
 namespace boost { namespace geometry
diff --git a/include/boost/geometry/multi/core/closure.hpp b/include/boost/geometry/multi/core/closure.hpp
index 46f79a18b..43bfa8c34 100644
--- a/include/boost/geometry/multi/core/closure.hpp
+++ b/include/boost/geometry/multi/core/closure.hpp
@@ -24,6 +24,11 @@ namespace boost { namespace geometry
 namespace core_dispatch
 {
 
+template <typename Multi>
+struct closure<multi_point_tag, Multi> : public core_detail::closure::closed {};
+
+template <typename Multi>
+struct closure<multi_linestring_tag, Multi> : public core_detail::closure::closed {};
 
 // Specialization for polygon: the closure is the closure of its rings
 template <typename MultiPolygon>