• Journal of the Korean Mathematical Society
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• v.35 no.1
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• pp.23-76
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• 1998

We prove that a non-empty separable metrizable space X admits a totally bounded metric for which the metric dimension of X in Assouad's sense equals the topological dimension of X, which leads to a characterization for the latter. We also give a characterization based on this Assouad dimension for the demension (embedding dimension) of a compact set in a Euclidean space. We discuss Assouad dimension and these results in connection with porous sets and measures with the doubling property. The elementary properties of Assouad dimension are proved in an appendix.

• Honam Mathematical Journal
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• v.35 no.3
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• pp.329-342
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• 2013

We study lightlike hypersurfaces M of a semi-Riemannian space form $\tilde{M}(c)$ with a semi-symmetric non-metric connection whose structure vector field is tangent to M. Our main result is two characterization theorems for such a lightlike hypersurface.

• Communications of the Korean Mathematical Society
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• v.28 no.4
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• pp.809-818
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• 2013

We study irrotational half lightlike submanifolds M of a semi-Riemannian space form with a semi-symmetric non-metric connection such that its structure vector field is tangent to M. We prove two characterization theorems for such an irrotational half lightlike submanifold.

• Kyungpook Mathematical Journal
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• v.63 no.4
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• pp.611-622
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• 2023

In this paper, we prove that every weakly Einstein slope metric, which is conformally flat on a manifold M of dimension n ≥ 3, is either a locally Minkowski metric or a Riemannian metric. We also prove the same result for conformally flat weakly Einstein Kropina metrics.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.1873-1886
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• 2013

In this paper, we characterize inner uniform domains in $\mathbb{R}^n$ in terms of Apollonian inner metric and the metric $j^{\prime}_D$ when D are Apollonian. As an application, a new characterization for A-uniform domains is obtained.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.1
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• pp.41-51
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• 2017

In this note, we deal with some characterizations of relative compactness on the $L_p$ metric space of fuzzy sets. And then, we point out that a characterization of relative compact subsets of fuzzy numbers with sendograph metric can be improved.

• Bulletin of the Korean Mathematical Society
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• v.33 no.1
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• pp.35-38
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• 1996

The aim of this paper is to present a characterization of Hilbert spaces in terms of the lengths of four sides and two diagonals of a parallelogram.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.05a
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• pp.277-280
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• 2002

In this paper, we characterize the Borel $\sigma$-field generated by the Hausdorff-Skorokhod metric on the space of normal and upper-semicontinuous fuzzy sets with compact support in the Ecleadean space R$\^$n/. As a result. we give a characterization of measurable fuzzy mappings .

• Bulletin of the Korean Mathematical Society
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• v.57 no.6
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• pp.1335-1349
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• 2020

In this paper, we give an equivalent characterization for general (α, β)-metrics with reversible geodesics when the dimension of the manifold is greater than 2.

• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.311-317
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• 2014

We study lightlike hypersurfaces of a semi-Riemannian space form $\tilde{M}(c)$ admitting a semi-symmetric non-metric connection. First, we construct a type of lightlike hypersurfaces according to the form of the structure vector field of $\tilde{M}(c)$, which is called a ascreen lightlike hypersurface. Next, we prove a characterization theorem for such an ascreen lightlike hypersurface endow with a totally geodesic screen distribution.