| 1. | The group topology is often finer than the relative topology.
|
| 2. | The topology generated by these bases is the relative topology.
|
| 3. | The conclusion is that the relative topology is the same as the group topology.
|
| 4. | In the relative topology on the Cantor set, the points have been separated by a clopen set.
|
| 5. | Equivalently, is an embedded Lie subgroup if and only if its group topology equals its relative topology.
|
| 6. | The submanifold topology on an immersed submanifold need not be the relative topology inherited from " M ".
|
| 7. | Pointed spaces are often taken as a special case of the relative topology, where the subset is a single point.
|
| 8. | Thus, much of homotopy theory is usually developed on pointed spaces, and then moved to relative topologies in algebraic topology.
|
| 9. | This is, by the way it is constructed, a neighborhood basis both in the group topology and the relative topology.
|
| 10. | :But there is no such a space, because A and B would be " closed " also in their union wrto the relative topology.
|
मोबाइल