• East Asian mathematical journal
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• v.22 no.2
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• pp.131-149
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• 2006

In this paper we introduce the concept of $\gamma$-preopen sets in a topological space together with its corresponding $\gamma$-preclosure and $\gamma$-preinterior operators and a new class of topology $\tau_{{\gamma}p}$ which is generated by the class of $\gamma$-preopen sets. Also we introduce $\gamma$-pre $T_i$ spaces(i=0, $\frac{1}{2}$, 1, 2) and study some of its properties and we proved that if $\gamma$ is a regular operation, then$(X,\;{\tau}_{{\gamma}p})$ is a $\gamma$-pre $T\frac{1}{2}$ space. Finally we introduce $(\gamma,\;\beta)$-precontinuous mappings and study some of its properties.

• Journal of the Korean Chemical Society
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• v.57 no.2
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• pp.176-203
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• 2013

In this work is induced a new topology of solutions of chemical equations by virtue of point-set topology in an abstract stoichiometrical space. Subgenerators of this topology are the coefficients of chemical reaction. Complex chemical reactions, as those of direct reduction of hematite with a carbon, often exhibit distinct properties which can be interpreted as higher level mathematical structures. Here we used a mathematical model that exploits the stoichiometric structure, which can be seen as a topology too, to derive an algebraic picture of chemical equations. This abstract expression suggests exploring the chemical meaning of topological concept. Topological models at different levels of realism can be used to generate a large number of reaction modifications, with a particular aim to determine their general properties. The more abstract the theory is, the stronger the cognitive power is.

• 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.

• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1285-1307
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• 2019

For a multiplication R-module M we consider the Zariski topology in the set Spec (M) of prime submodules of M. We investigate the relationship between the algebraic properties of the submodules of M and the topological properties of some subspaces of Spec (M). We also consider some topological aspects of certain frames. We prove that if R is a commutative ring and M is a multiplication R-module, then the lattice Semp (M/N) of semiprime submodules of M/N is a spatial frame for every submodule N of M. When M is a quasi projective module, we obtain that the interval ${\uparrow}(N)^{Semp}(M)=\{P{\in}Semp(M){\mid}N{\subseteq}P\}$ and the lattice Semp (M/N) are isomorphic as frames. Finally, we obtain results about quantales and the classical Krull dimension of M.

• Proceedings of the Korean Vacuum Society Conference
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• 2010.02a
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• pp.14-15
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• 2010

Recently there has been growing interest in topological insulators or the quantum spin Hall (QSH) phase, which are insulating materials with bulk band gaps but have metallic edge states that are formed topologically and robust against any non-magnetic impurity [1]. In a three-dimensional material, the two-dimensional surface states correspond to the edge states (topological metal) and their intriguing nature in terms of electronic and spin structures have been experimentally observed in bulk Bi1-xSbx single crystals [2,3,4]. However, if we want to know the transport properties of these topological metals, high purity samples as well as very low temperature will be needed because of the contribution from bulk states or impurity effects. In a recent report, it was also shown that an intriguing coupling between the surface and bulk states will occur [5]. A simple solution to this bothersome problem is to prepare a topological metal on an ultrathin film, in which the surface-to-bulk ratio is drastically increased. Therefore in the present study, we have investigated if there is a method to make an ultrathin Bi1-xSbx film on a semiconductor substrate. From reflection high-energy electron diffraction observation, it was found that single crystal Bi1-xSbx films (0${\sim}30\;{\AA}A$ can be prepared on Si(111)-$7{\times}7$. The transport properties of such films were characterized by in situ monolithic micro four-point probes [6]. The temperature dependence of the resistivity for the x=0.1 samples was insulating when the film thickness was $240\;{\AA}A$. However, it became metallic as the thickness was reduced down to $30\;{\AA}A$, indicating surface-state dominant electrical conduction. Figure 1 shows the Fermi surface of $40\;{\AA}A$ thick Bi0.92Sb0.08 (a) and Bi0.84Sb0.16 (b) films mapped by angle-resolved photoemission spectroscopy. The basic features of the electronic structure of these surface states were shown to be the same as those found on bulk surfaces, meaning that topological metals can be prepared at the surface of an ultrathin film. The details will be given in the presentation.

• The Mathematical Education
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• v.25 no.1
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• pp.9-13
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• 1986

• Bulletin of the Korean Mathematical Society
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• v.10 no.1
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• pp.7-8
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• 1973

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.579-591
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• 2015

Properties of prime filters are studied in BE-algebras as well as in commutative BE-algebras. An equivalent condition is derived for a BE-algebra to become a totally ordered set. A condition L is introduced in a commutative BE-algebra in ordered to study some more properties of prime filters in commutative BE-algebras. A set of equivalent conditions is derived for a commutative BE-algebra to become a chain. Some topological properties of the space of all prime filters of BE-algebras are studied.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1069-1077
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• 2013

Several authors investigated the properties which are invariant under the passage from a group to its nonabelian tensor square. In the present note we study this problem from the viewpoint of the classes of groups and the methods allow us to prove a result of invariance for some geometric properties of discrete groups.

• Kyungpook Mathematical Journal
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• v.57 no.2
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• pp.199-210
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• 2017

In this paper, we analyze some new properties of nowhere dense and strongly nowhere dense sets. Also, we discuss the images of nowhere dense and strongly nowhere dense sets. Further, we study the properties of weak Baire space in generalized topological spaces.