On the topology of -normed spaces with respect to norms of its quotient spaces
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In this paper, we study some topological characteristics of n-normed spaces. We construct quotient spaces of an n-normed space and de ne a norm in each quotient space. Using these norms, we observe convergence sequences, closed sets, and bounded sets in n-normed spaces. These norms will be a new viewpoint in observing the characteristics of n-normed spaces. We also review the completeness of n- normed spaces.
Abstract
In this paper, we study some topological characteristics of n-normed spaces. We construct quotient spaces of an n-normed space and de ne a norm in each quotient space. Using these norms, we observe convergence sequences, closed sets, and bounded sets in n-normed spaces. These norms will be a new viewpoint in observing the characteristics of n-normed spaces. We also review the completeness of n- normed spaces.
참고문헌 (14)
- H. Batkunde, "n-Normed spaces with norms of its quotient spaces", J. Phys.: Conf. Series, 1097, pp.012079~ (2018)
- H. Batkunde, "Bounded linear functionals on the n-normed space of p-summable sequences", Acta Univ. M. Belii. Ser. Math, 21, pp.66~75 (2013)
- H. Batkunde, "Bounded 2-linear functionals on the n-normed spaces", J. Phys.: Conf. Series, 893, pp.12~16 (2017)
- S. Ekariani, "A contractive mapping theorem on the n-normed space of p-summable sequences", J. Math. Analysis, 4(1), pp.1~7 (2013)
- R. W. Fresse, "Geometry of Linear 2-Normed Spaces" (2001), Nova Publishers
- S. Gahler, "Lineare 2-normierte raume", Math. Nachr, 28, pp.1~13 (1964)
- S. Gahler, "Untersuchungen uber verallgemeinerte m-metrische raume I", Math. Nachr, 40, pp.165~189 (1969)
- S. Gahler, "Untersuchungen uber verallgemeinerte m-metrische raume II", Math. Nachr, 40, pp.229~264 (1969)
- S. Gahler, "Untersuchungen uber verallgemeinerte m-metrische raume III", Math. Nachr, 41, pp.23~36 (1969)
- H. Gunawan, "On n-normed spaces", Int. J. Math. Math. Sci, 27, pp.631~639 (2001)
- H. Gunawan, "Inner products on n-inner product spaces", Soochow J. Math, 28, pp.389~398 (2002)
- H. Gunawan, "Fixed point theorems on bounded sets in an n-normed space", J. Math. Anal, 3, pp.51~58 (2015)
- S.R. Meitei, "On bounded n-linear operators", J. Math. Comput. Sci, 8(2), pp.196~215 (2018)
- J. K. Srivastava, "On some Cauchy sequences defined in `p considered as n-normed space", J. Rajashtan Acad. Phys. Sci, 15, pp.107~116 (2016)