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 .
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