Last-modified: 2012-10-04 (木) 14:33:34
- A topological space (X,τ) is said to be p-regular if for each closed set F of X and each point , there exist disjoint pre-open? sets U and V such that .
- For a topological space (X,τ) the following are equivalent:
- X is p-regular.
- For each x in X and each open set U of X containing x, there exists pre-open? set V such that .
- For each closed set F of X,
- For each subset A of X and each open set U of X such that , there exists pre-openset? V such taht .
- For each nonempty subset A of X and each closed set F of X such tant , there exist pre-open? sets V and W such that .
- The product space of p-regular spaces is p-regular.
- If X is a p-regular space and X' is an α-set of X, then the subspace X' is p-regular.
- El-Deeb, N.; Hasanein, I. A.; Mashhour, A. S.; Noiri, T. , On p-regular spaces., Bull. Math. Soc. Sci. Math. R. S. Roumanie (N.S.) 27(75) (1983), no. 4, 311–315.