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
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[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).
[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
[1]
M. Caldas Cueva, S. Jafari, N. Rajesh, and M. L. Thivagar, “On ĝ-homeomorphisms in topological spaces”, Proyecciones (Antofagasta, On line), vol. 28, no. 1, pp. 1-19, 1.
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