Abstract
The aim of this paper is to introduce a new class of continuous multifunctions, namely upper and lower na-continuous multifunctions, and to obtain some characterizations concerning upper and lower nacontinuous multifunctions. The authors investigate the graph of upper and lower na-continuous multifunctions, and the preservation of properties under upper na-continuous multifunctions. Also, the relationship between upper and lower na-continuous multifunctions and some known types of continuous multifunctions are discussed.
Keywords
α-open sets δ-open sets multifunctions α-compact spaces δ-connected spaces 2010 AMS Classification: 54 C 60
References
- Akda˘g, M. On super continuous multifunctions, Acta Math. Hungar. 99 (1-2), 143–153, 2003. [2] Akda˘g, M. Weak and strong forms of continuity of multifunctions, Chaos Solitions and Fractals 32, 1337–1344, 2007.
- Banzaru, T. On the upper semicontinuity of the upper topological limit for multifunction nets, Semin. Mat. Fiz. Inst. Politeh Timisoara, 59–64, 1983.
- Berge, C. Escapes topologiques fonctions multivoques (Dunod, Paris, 1959)
- Chae, G. U. Noiri, T. and Lee, D. W. On na-continuous functions, Kyungpook Math. J. 26(1), 73–79, 1986.
- Maheswari, S. N. and Thakur, S. S. On α-compact spaces, Bull. Inst. Sinica 13, 341–347, 1985. [7] Navalagi, G. B. α-Neighbourhoods, unpublished.
- Neubrunn, T. Strongly quasi continuous multivalued mappings, General topology and its relations to modern analysis and algebra VI. Proc of Symposium, Prague, 1986, Helderman Verlag.
- Nijastad, O. On some classes of nearly open sets, Pacific J. Math. 15, 961–970, 1965.
- Noiri, T. On δ-continuous functions, J. Korean Math. Soc. 16, 161–166, 1980.
- Noiri, T. and Popa, V. Almost weakly continuous multifunctions, Demonstratio Math. 26(2), 363–380, 1993.
- Noiri, T. Popa, V. On upper and lower M-continuous multifunctions, FILOMAT 14, 73-86, 2000. [13] Ponomarev, V. I. Properties of topological spaces preserved under multivalued continuous mappings, Amer. Math. Soc. Transl. 38 (2), 119–140, 1964.
- Singal, M. K. and Mathur, A. On nearly compact spaces, Bull. Un. Mat. Ital. 4 (2), 702–710, 1969. [15] Stone, M. H. Applications of the theory of Boolean rings to general topology, T. A. M. S. 41, 375–381, 1937.
- Velicko, N. V. H-closed topological spaces, Amer. Math. Soc. Transl. 78, 103–118, 1968.
Abstract
References
- Akda˘g, M. On super continuous multifunctions, Acta Math. Hungar. 99 (1-2), 143–153, 2003. [2] Akda˘g, M. Weak and strong forms of continuity of multifunctions, Chaos Solitions and Fractals 32, 1337–1344, 2007.
- Banzaru, T. On the upper semicontinuity of the upper topological limit for multifunction nets, Semin. Mat. Fiz. Inst. Politeh Timisoara, 59–64, 1983.
- Berge, C. Escapes topologiques fonctions multivoques (Dunod, Paris, 1959)
- Chae, G. U. Noiri, T. and Lee, D. W. On na-continuous functions, Kyungpook Math. J. 26(1), 73–79, 1986.
- Maheswari, S. N. and Thakur, S. S. On α-compact spaces, Bull. Inst. Sinica 13, 341–347, 1985. [7] Navalagi, G. B. α-Neighbourhoods, unpublished.
- Neubrunn, T. Strongly quasi continuous multivalued mappings, General topology and its relations to modern analysis and algebra VI. Proc of Symposium, Prague, 1986, Helderman Verlag.
- Nijastad, O. On some classes of nearly open sets, Pacific J. Math. 15, 961–970, 1965.
- Noiri, T. On δ-continuous functions, J. Korean Math. Soc. 16, 161–166, 1980.
- Noiri, T. and Popa, V. Almost weakly continuous multifunctions, Demonstratio Math. 26(2), 363–380, 1993.
- Noiri, T. Popa, V. On upper and lower M-continuous multifunctions, FILOMAT 14, 73-86, 2000. [13] Ponomarev, V. I. Properties of topological spaces preserved under multivalued continuous mappings, Amer. Math. Soc. Transl. 38 (2), 119–140, 1964.
- Singal, M. K. and Mathur, A. On nearly compact spaces, Bull. Un. Mat. Ital. 4 (2), 702–710, 1969. [15] Stone, M. H. Applications of the theory of Boolean rings to general topology, T. A. M. S. 41, 375–381, 1937.
- Velicko, N. V. H-closed topological spaces, Amer. Math. Soc. Transl. 78, 103–118, 1968.
Details
| Primary Language | English |
|---|---|
| Subjects | Statistics |
| Journal Section | Mathematics |
| Authors | |
| Publication Date | February 1, 2011 |
| Published in Issue | Year 2011 Volume: 40 Issue: 2 |