3 ms·
Continuity in the topological sense implies continuity by limits. For topological spaces with a countable (local) basis, the converse is also true. So, in gene
by dirkt 11y ago
Continuity in the topological sense implies continuity by limits. For topological spaces with a countable (local) basis, the converse is also true.
So, in general it's not equivalent. For the reals etc., it is.
- cottonseed 11y agoThey are equivalent if you consider limits of nets rather than limits of sequences.