Assertion: abelian group's subgroup | /r/HasProperty | closed
Facets:
value: conversely
type: DEGREE
value: in g
type: LOCATION
value: in the topological
type: LOCATION
Source sentences:
text: If the subgroup N {\displaystyle N} is closed (in the topological rather than the algebraic sense of the word), then the dimension of a Lie group or homogeneous space G {\displaystyle G}
text: For a linear algebraic group G {\displaystyle G} its Borel subgroup is defined as a subgroup which is closed, connected, and solvable in G {\displaystyle G} , and it is the maximal possible subgroup with these properties (note the second two are topological properties).
text: Conversely, every locally compact subgroup of a Hausdorff group is closed.
text: every discrete subgroup of a Hausdorff group is closed.