• Communications of the Korean Mathematical Society
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• v.26 no.2
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• pp.291-296
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• 2011

Cs$\'{a}$sz$\'{a}$r [3] introduced the notions of ${\gamma}$-compact and ${\gamma}$-operation on a topological space. In this paper, we introduce the notions of almost ${\Gamma}$-compact, (${\gamma},{\tau}$)-continuous function and (${\gamma},{\tau}$)-open function defined by ${\gamma}$-operation on a topological space and investigate some properties for such notions.

• Bulletin of the Korean Mathematical Society
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• v.41 no.3
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• pp.457-464
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• 2004

Let X be a Banach space and Z a closed subspace of a Banach space Y. Denote by Ｌ(X, Y) the space of all bounded linear operators from X to Y and by Ｋ(X, Y) its subspace of compact linear operators. Using Hahn-Banach extension operators corresponding to ideal projections, we prove that if either $X^{**}$ or $Y^{*}$ has the Radon-Nikodym property and Ｋ(X, Y) is an M-ideal (resp. an HB-subspace) in Ｌ(X, Y), then Ｋ(X, Z) is also an M-ideal (resp. HB-subspace) in Ｌ(X, Z). If Ｌ(X, Y) has property SU instead of being an M-ideal in Ｌ(X, Y) in the above, then Ｋ(X, Z) also has property SU in Ｌ(X, Z). If X is a Banach space such that $X^{*}$ has the metric compact approximation property with adjoint operators, then M-ideal (resp. HB-subspace) property of Ｋ(X, Y) in Ｌ(X, Y) is inherited to Ｋ(X, Z) in Ｌ(X, Z).

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1067-1075
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• 1996

We show that every ultrapure space is weakly star reducible, and that every countably compact weakly star reducible space is compact. We also pose open problems.

• Journal of Creative Information Culture
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• v.5 no.3
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• pp.345-353
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• 2019

Several studies have been proposed to improve storage space efficiency by expressing binary trie data structure as a linear binary bit string. Compact binary tree approach generated using one binary trie increases the key search time significantly as the binary bit string becomes very long as the size of the input key set increases. In order to reduce the key search range, a hierarchical compact binary tree technique that hierarchically expresses several small binary compact trees has been proposed. The search time increases proportionally with the number and length of binary bit streams. In this paper, we generate several binary compact trees represented by full binary tries hierarchically. The search performance is improved by allowing a path for the binary bit string corresponding to the search range to be determined through simple numeric conversion. Through the performance evaluation using the worst time and space complexity calculation, the proposed method showed the highest performance for retrieval and key insertion or deletion. In terms of space usage, the proposed method requires about 67% ~ 68% of space compared to the existing methods, showing the best space efficiency.

• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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• pp.235-239
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• 2004

Vaughan proved that if X is countably compact, then the Alexandroff duplicate A(X) is acc. In this note, we give an example to show that the result can not be generalized to star-Lindelof spaces. Moreover, we give a positive result.

• Kyungpook Mathematical Journal
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• v.28 no.1
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• pp.91-95
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• 1988

The nature of a H-set in a Hausdorff space is not well understood. In this note it is shown that if X is a countable union of nowhere dense compact sets, then X is not H-embeddable in any Hausdorff space. An example is given to show that there exists a non-Urysohn, non-H-closed space X such that each H-set of X is compact.

• Korean Institute of Interior Design Journal
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• v.19 no.2
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• pp.126-135
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• 2010

As public space such as plaza and square in the compact city type multi-use complex is a social public space that various communication and cultural exchange take places in city environment. The purpose of this study is to analyse and categorize the design elements as a valuation basis for the public space in the compact city type multi-use complex. The scope of contents of this study is focused on the Central City, COEX and Western Dome facilities in Korea. This study review based on the previous studies and statistical analysis about questionnaires obtained from 131 users of three facilities were conducted for this study. The results of the survey as follows accessibility, comfort, exchange were extracted as the aspects for evaluation for functional activity and connection, openness, hierarchy were extracted as the aspects for evaluation for space formation. The K facility's priority aspect is the accessibility and the S and the W facilities' are the openness.

• Journal of the Korean Mathematical Society
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• v.54 no.1
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• pp.281-302
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• 2017

For a Banach space operator $A{\in}B(\mathcal{X})$, let ${\sigma}(A)$, ${\sigma}_a(A)$, ${\sigma}_w(A)$ and ${\sigma}_{aw}(A)$ denote, respectively, its spectrum, approximate point spectrum, Weyl spectrum and approximate Weyl spectrum. The operator A is polaroid (resp., left polaroid), if the points $iso{\sigma}(A)$ (resp., $iso{\sigma}_a(A)$) are poles (resp., left poles) of the resolvent of A. Perturbation by compact operators preserves neither SVEP, the single-valued extension property, nor the polaroid or left polaroid properties. Given an $A{\in}B(\mathcal{X})$, we prove that a sufficient condition for: (i) A+K to have SVEP on the complement of ${\sigma}_w(A)$ (resp., ${\sigma}_{aw}(A)$) for every compact operator $K{\in}B(\mathcal{X})$ is that ${\sigma}_w(A)$ (resp., ${\sigma}_{aw}(A)$) has no holes; (ii) A + K to be polaroid (resp., left polaroid) for every compact operator $K{\in}B(\mathcal{X})$ is that iso${\sigma}_w(A)$ = ∅ (resp., $iso{\sigma}_{aw}(A)$ = ∅). It is seen that these conditions are also necessary in the case in which the Banach space $\mathcal{X}$ is a Hilbert space.

• Korean Journal of Mathematics
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• v.29 no.3
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• pp.555-561
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• 2021

In this paper, we investigate some properties of countably g-compact and sequentially GO-compact spaces. Also, we discuss the relation between countably g-compact and sequentially GO-compact. Next, we introduce the definition of g-subspace and study the characterization of g-subspace.

• Bulletin of the Korean Mathematical Society
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• v.41 no.4
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• pp.665-676
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• 2004

In this paper we characterize asymptotic stability via Lyapunov function in general dynamical systems on c-first countable space. We give a family of examples which have first countable but not c-first countable, also c-first countable and locally compact space but not metric space. We obtain several necessary and sufficient conditions for a compact subset M of the phase space X to be asymptotic stability.