- Volume 29 Issue 4
A set with an operation defined on a family of subsets is studied. The operation is used to generalize the topological space itself. The operation defines the operation-open subsets in the set. Relations are studied among two types of the interiors and the closures of subsets. Some properties of maximal operation-open sets are obtained. Semi-open sets and pre-open sets are defined in the sets with operations and some relations among them are proved.
D. S. Jankovic, On functions with
$\alpha$-closed graphs, Glas. Mat. Ser. III 18(38) (1983), no. 1, 141-148.
- S. Kasahara, Operation-compact spaces, Math. Japon. 24 (1979), no. 1, 97-105.
- J. L. Kelley, General Topology, D. Van Nostrand Company, Inc., Toronto-New York- London, 1955.
- A. S. Mashhour, A. A. Allam, F. S. Mahmoud, and F. H. Khedr, On supratopological spaces, Indian J. Pure Appl. Math. 14 (1983), no. 4, 502-510.
- H. Maki, K. Chandrasekhara Rao, and A. Nagoor Gani, On generalizing semi-open sets and preopen sets, Pure Appl. Math. Sci. 49 (1999), no. 1-2, 17-29.
- H. Ogata, Operations on topological spaces and associated topology, Math. Japon. 36 (1991), no. 1, 175-184.
- V. Popa and T. Noiri, On the definitions of some generalized forms of continuity under minimal conditions, Mem. Fac. Sci. Kochi Univ. Ser. A Math. 22 (2001), 9-18.
- F. U. Rehman and B. Ahmad, Operations on topological spaces-I, Math. Today 10 (1992), 29-36.
Supported by : JSPS