On a Characterisation of the System of all regularly closed Sets in general closure spaces
✍ Scribed by Milan Sekanina
- Publisher
- John Wiley and Sons
- Year
- 1968
- Tongue
- English
- Weight
- 288 KB
- Volume
- 38
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
✦ Synopsis
I n several questions concerning connections between general topologies and BOOLEAN algebras systems regularly open or closed sets play an important role. The lattice-theoretical characterisations of these systems are known for general topological spaces. Problem 81 in [I] and the paper [ 2 ] deal with such a characterisation for certain classes of topological spaces. Following paper contains a characterisation of the system of all regularly closed sets in general closure spaces. Corresponding results on regularly open sets can be obtained by the fact that a subset of general closure space is regularly open iff its complement is regularly closed.