SEMI-HOMOTOPY AND SEMI-FUNDAMENTAL GROUPS

Year 2016, Volume: 4 Issue: 1, 155 - 163, 01.04.2016

Ayhan Erciyes , Ali Aytekin Tunçar Şahan

Abstract

In this study we introduce the notions of semi-homotopy of semi- continuous maps and of semi-paths. We also construct a group structure, which will be called semi-fundamental group, using semi-loops and explore some properties of semi-homotopy and semi-fundamental groups.

Keywords

Semi-open sets, semi-closed sets, homotopy, fundamental groups

References

• [1] Bhattacharyya, P. and Lahiri, B.K., Semi-generalized closed sets in topology, lnd. Jr. Math., 29 (1987), 375{382.
• [2] Brown, R., Topology and groupoids, BookSurge LLC, North Carolina, 2006.
• [3] Csaszar, A., Generalized open sets, Acta Mathematica Hungarica, 75(1), (1997), 65{87.
• [4] Crossley, S. and Hildebrand, S.K., Semi-closure, Texas J. Sci. 22 (1971), 99{112.
• [5] Crossley, S. and Hildebrand, S.K., Semi-topological properties, Fundamenta Mathematicae 74(3) (1972), 233{254.
• [6] Hatcher, A., Algebraic topology, Cambridge University Press, 2002.
• [7] Levine, N., Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly 70 (1963), 36{41.
• [8] Maheshawari, S.M.N. and Prasad, R., Some new separation axioms, Ann. Soco. Sci. Bruxelles 89 (1975), 395{402.
• [9] Rotman, J.J., An introduction to algebraic topology, Springer, 1988.
• [10] Scheers, J.M., An exploration of semi-open sets in topological spaces, M.Sc. Thesis, Stephen F. Austin State University, 2011.