On ĝ-homeomorphisms in topological spaces
DOI:
https://doi.org/10.4067/S0716-09172009000100001Keywords:
ge-closed set, ge-open set, ge-continuous function, ge-irresolute map.Abstract
In this paper, we first introduce a new class of closed map called ĝ-closed map. Moreover, we introduce a new class of homeomorphism called ĝ-homeomorphism, which are weaker than homeomorphism. We prove that gc-homeomorphism and ĝ-homeomorphism are independent. We also introduce ĝ*-homeomorphisms and prove that the set of all ĝ*-homeomorphisms forms a group under the operation of composition of maps.
References
[2] Devi R, Balachandran K and Maki H, Semi-generalized homeomorphisms and generalized semi-homeomorphisms in topological spaces, Indian J. Pure Appl. Math., 26, pp. 271-284, (1995).
[3] Devi R, Maki H and Balachandran K, Semi-generalized closed maps and generalized semi-closed maps, Mem. Fac. Kochi Univ. Ser. A. Math., 14, pp. 41-54, (1993).
[4] Jafari S, Noiri T, Rajesh N and Thivagar M. L, Another generalization of closed sets. (Submitted). [5] Jänich K, Topologie, Springer-Verlag, Berlin, 1980 (English translation).
[6] Levine N, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70, pp. 36-41, (1963).
[7] Levine N, Generalized closed sets in topology, Rend. Circ. Math. Palermo, (2) 19, pp. 89-96; (1970).
[8] Maki H, Devi R and Balachandran K, Generalized α-closed sets in topology, Bull. Fukuoka Univ. Ed Part III, 42, pp. 13-21, (1993).
[9] Maki H, Sundram P and Balachandran K, On generalized homeomorphisms in topological spaces, Bull. Fukuoka Univ. Ed. Part III, 40, pp. 13-21, (1991).
[10] Mashhour A. S, Abd. El-Monsef M. E and El-Deeb S. N, On precontinuous and weak precontinuous mappings, Proc. Math. Phys, Soc. Egypt, 53, pp. 47-53, (1982).
[11] Njastad O, On some classes of nearly open sets, Pacific J. Math. 15, pp. 961-970, (1965).
[12] Malghan S. R, Generalized closed maps, J. Karnataka Univ. Sci., 27, pp. 82-88, (1982).
[13] Rajesh N and Ekici E, On a new form of irresoluteness and weak forms of strong continuity (submitted).
[14] Rajesh N and Ekici E, On g e-locally closed sets in topological spaces. Kochi. J of Math. Vol.2 (to appear), (2007).
[15] Rajesh N and Ekici E, On g e-continuous mappings in topological spaces. Proc. Inst. Math. (God. Zb. Inst. Mat.)., Skopje (to appear).
[16] Rajesh N and Ekici E, On a decomposition of T1/2-spaces, Math. Maced. (to appear).
[17] Stone M, Application of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc. 41, pp. 374-481, (1937).
[18] Sundaram P, Studies on generalizations of continuous maps in topological spaces, Ph.D. Thesis, Bharathiar University, Coimbatore (1991).
[19] Veera Kumar M. K. R. S, gb-closed sets in topological spaces, Bull. Allahabad Math. Soc., 18, pp. 99-112, (2003).
[20] Veera Kumar M. K. R. S, Between g*-closed sets and g-closed sets, Antarctica J. Math, Reprint.
[21] Veera Kumar M. K. R. S, #g-semi-closed sets in topological spaces, Antarctica J. Math, 2(2), pp. 201-222, (2005).
How to Cite
Issue
Section
-
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.