sage.manifolds.closure_topological_submanifold, TopologicalSubmanifol…

…d.closure: New

src/sage/manifolds/closure_topological_submanifold.py

@@ -0,0 +1,31 @@
+r"""
+Topological closures of embedded submanifolds
+"""
+
+from sage.manifolds.subset import ManifoldSubset
+
+class ClosureOfTopologicalSubmanifold(ManifoldSubset):
+
+    def __init__(self, submanifold, name=None, latex_name=None):
+
+        self._submanifold = submanifold
+        base_manifold = submanifold.embedding().codomain()
+        if name is None:
+            name = 'cl_' + submanifold._name
+        if latex_name is None:
+            if name is None:
+                latex_name = r'\mathop{\mathrm{cl}}(' + submanifold._latex_name + ')'
+            else:
+                latex_name = name
+        ManifoldSubset.__init__(self, base_manifold, name, latex_name=latex_name)
+
+    def _repr_(self):
+        r"""
+        String representation of the object.
+
+        TESTS::
+
+        """
+        return "Topological closure {} of the {}".format(self._name, self._submanifold)
+
+

src/sage/manifolds/topological_submanifold.py

@@ -747,3 +747,25 @@ def embedding(self):
         if not self._embedded:
             raise ValueError("the submanifold is not embedded")
         return self._immersion
+
+    def closure(self):
+        r"""
+        Return the topological closure of ``self`` as a subset of the ambient manifold.
+
+        EXAMPLES::
+
+            sage: M = Manifold(2, 'M', structure="topological")
+            sage: N = Manifold(1, 'N', ambient=M, structure="topological")
+            sage: CM.<x,y> = M.chart()
+            sage: CN.<u> = N.chart()
+            sage: CN.add_restrictions([u > -1, u < 1])
+            sage: phi = N.continuous_map(M, {(CN,CM): [u, u^2]})
+            sage: N.set_embedding(phi)
+            sage: N
+            1-dimensional topological submanifold N embedded in the 2-dimensional topological manifold M
+            sage: N.closure()
+            Topological closure cl_N of the 1-dimensional topological submanifold N embedded in the 2-dimensional topological manifold M
+
+        """
+        from .closure_topological_submanifold import ClosureOfTopologicalSubmanifold
+        return ClosureOfTopologicalSubmanifold(self)