R
- Refinement
- A cover K is a refinement of a cover L if every member of K is a subset of some member of L.
- Regular
- A space is regular if, whenever C is a closed set and x is a point not in C, then C and x have disjoint neighbourhoods.
- Regular Hausdorff
- A space is regular Hausdorff (or T3) if it is a regular T0 space. (A regular space is Hausdorff if and only if it is T0, so the terminology is consistent.)
- Regular open
- An open subset U of a space X is regular open if it equals the interior of its closure. An example of a non-regular open set is the set U = (0, 1) U (1, 2) in R with its normal topology, since 1 is in the interior of the closure of U, but not in U. The regular open subsets of a space form a complete Boolean algebra.
- Relatively compact
- A subset Y of a space X is relatively compact in X if the closure of Y in X is compact.
- Residual
- If X is a space and A is a subset of X, then A is residual in X if the complement of A is meagre in X. Also called comeagre or comeager.
- Resolvable
- A topological space is called resolvable if it is expressible as the union of two disjoint dense subsets.
- Rim-compact
- A space is rim-compact if it has a base of open sets whose boundaries are compact.
Read more about this topic: Glossary Of Topology