• Communications of the Korean Mathematical Society
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• v.25 no.3
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• pp.477-484
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• 2010

In this paper, we introduce a new property (*) of a topological space and prove that if X satisfies one of the following conditions (1) and (2), then compactness, countable compactness and sequential compactness are equivalent in X; (1) Each countably compact subspace of X with (*) is a sequential or AP space. (2) X is a sequential or AP space with (*).

• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.581-590
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• 2014

In approach theory, we can provide arbitrary products of ${\infty}p$-metric spaces with a natural structure, whereas, classically only if we rely on a countable product and the question arises, then, whether properties which are derived from countability properties in metric spaces, such as sequential and countable compactness, can also do away with countability. The classical results which simplify the study of compactness in pseudometric spaces, which proves that all three of the main kinds of compactness are identical, suggest a further study of the category $pMET^{\infty}$.

• Korean Journal of Mathematics
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• v.5 no.2
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• pp.211-215
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• 1997

In this paper, we introduce two notions of compactness defined by sequential convergence and compare them.

• The Pure and Applied Mathematics
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• v.25 no.4
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• pp.243-252
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• 2018

In this paper, we study the sequentially open and closed subsets of sequential topological groups determined by sequentially continuous group homomorphism. In particular, we investigate the sequentially openness (closedness) and sequentially compactness of subsets of sequential topological groups by the aid of sequentially continuity, sequentially interior or closure operators. Moreover, we explore subgroup and sequential quotient group of a sequential topological group.

• 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.

• Communications of the Korean Mathematical Society
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• v.24 no.1
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• pp.145-152
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• 2009

In this paper, we introduce a new property of a topological space which is weaker than sequential compactness and give some necessary and sufficient conditions for a $Fr{\acute{e}}chet$-Urysohn space with the property to be sequentially compact.

• Journal of the Korean Mathematical Society
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• v.44 no.2
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• pp.261-273
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• 2007

In this paper, we introduce some new properties of a topological space which are respectively generalizations of $Fr\'{e}chet$-Urysohn property. We show that countably AP property is a sufficient condition for a space being countable tightness, sequential, weakly first countable and symmetrizable, to be ACP, $Fr\'{e}chet-Urysohn$, first countable and semimetrizable, respectively. We also prove that countable compactness is a sufficient condition for a countably AP space to be countably $Fr\'{e}chet-Urysohn$. We then show that a countably compact space satisfying one of the properties mentioned here is sequentially compact. And we show that a countably compact and countably AP space is maximal countably compact if and only if it is $Fr\'{e}chet-Urysohn$. We finally obtain a sufficient condition for the ACP closure operator $[{\cdot}]_{ACP}$ to be a Kuratowski topological closure operator and related results.

• BMB Reports
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• v.32 no.6
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• pp.521-528
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• 1999

The folding of recombinant hepatitis B virus X-protein (rHBx) solubilized from Escherichia coli inclusion bodies was investigated. By sequential dialysis of urea, rHBx was folded into its native structure, which was demonstrated by the efficacy of its transcriptional activation of the adenovirus major late promoter (MLP), fluorescence spectroscopy, and circular dichroism (CD) analysis. The decrease in CD values at 220 nm and a corresponding blue shift of the intrinsic fluorescence emission confirmed the ability of rHBx to refold in lower concentrations of urea, yielding the active protein. Equilibrium and kinetic studies of the refolding of rHBx were carried out by tryptophan fluorescence measurements. From the biphasic nature of the fluorescence curves, the existence of stable intermediate states in the renaturation process was inferred. Reverse phase-high performance liquid chromatography (RP-HPLC) analysis further demonstrated the existence of these intermediates and their apparent compactness.

• BMB Reports
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• v.39 no.3
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• pp.319-328
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• 2006

SecA protein, a cytoplasmic ATPase, plays a central role in the secretion of signal peptide-containing proteins. Here, we examined effects of signal peptide and ATP on the oligomerization, conformational change, and membrane binding of SecA. The wild-type (WT) signal peptide from the ribose-binding protein inhibited ATP binding to soluble SecA and stimulated release of ATP already bound to the protein. The signal peptide enhanced the oligomerization of soluble SecA, while ATP induced dissociation of SecA oligomer. Analysis of SecA unfolding with urea or heat revealed that the WT signal peptide induces an open conformation of soluble SecA, while ATP increased the compactness of SecA. We further obtained evidences that the signal peptide-induced oligomerization and the formation of open structure enhance the membrane binding of SecA, whereas ATP inhibits the interaction of soluble SecA with membranes. On the other hand, the complex of membrane-bound SecA and signal peptide was shown to resume nucleotide-binding activity. From these results, we propose that the translocation components affect the degree of oligomerization of soluble SecA, thereby modulating the membrane binding of SecA in early translocation pathway. A possible sequential interaction of SecA with signal peptide, ATP, and cytoplasmic membrane is discussed.