• Honam Mathematical Journal
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• v.33 no.2
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• pp.279-300
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• 2011

For a subset system M on any poset, M-Scott notions, such as M-way below relation,M-continuity,M-Scott convergence (of nets and filters respectively) and M-Scott topology are proposed Any approximating auxiliary relation on a poset can be represented by an M-way below relation such that this poset is M-continuous. It is shown that a poset is M-continuous iff the M-Scott topology is completely distributive. The topology induced by the M-Scott convergence coincides with the M-Scott topology. If the M-way below relation satisfies the property of interpolation then a poset is M-continuous if and only if the M-Scott convergence coincides with the M-Scott topological convergence. Also, M-continuity is characterized by a certain Galois connection.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.3
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• pp.415-424
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• 2012

As a generalization of countably approximating posets, we introduce the concept of generalized countably approximating posets. Some properties of generalized countably approximating posets are presented.

• Kyungpook Mathematical Journal
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• v.57 no.3
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• pp.385-391
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• 2017

In this paper, we study the notion of $z^J$ - ideals of posets and explore the various properties of $z^J$-ideals in posets. The relations between topological space on Sspec(P), the set $I_Q=\{x{\in}P:L(x,y){\subseteq}I\text{ for some }y{\in}P{\backslash}Q\}$ for an ideal I and a strongly prime ideal Q of P and $z^J$-ideals are discussed in poset P.

• Communications of the Korean Mathematical Society
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• v.28 no.1
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• pp.79-85
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• 2013

The structure of a poset P with smallest element 0 is looked at from two view points. Firstly, with respect to the Zariski topology, it is shown that Spec(P), the set of all prime semi-ideals of P, is a compact space and Max(P), the set of all maximal semi-ideals of P, is a compact $T_1$ subspace. Various other topological properties are derived. Secondly, we study the semi-ideal-based zero-divisor graph structure of poset P, denoted by $G_I$ (P), and characterize its diameter.

• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1265-1283
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• 2019

We develop a framework to construct geometric representations of finite groups G through the correspondence between real toric spaces $X^{\mathbb{R}}$ and simplicial complexes with characteristic matrices. We give a combinatorial description of the G-module structure of the homology of $X^{\mathbb{R}}$. As applications, we make explicit computations of the Weyl group representations on the homology of real toric varieties associated to the Weyl chambers of type A and B, which show an interesting connection to the topology of posets. We also realize a certain kind of Foulkes representation geometrically as the homology of real toric varieties.