• 충청수학회지
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• 제26권1호
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• pp.53-69
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• 2013

Topology may described a pattern of existence of elements of a given set X. The family ${\tau}(X)$ of all topologies given on a set X form a complete lattice. We will give some topologies on this lattice ${\tau}(X)$ using a topology on X and regard ${\tau}(X)$ a topological space. A topology ${\tau}$ on X can be regarded a map from X to ${\tau}(X)$ naturally. Such a map will be called topology field. Similarly we can also define pe-topology field. If X is a topological flow group with acting group T, then naturally we can get a another topological flow ${\tau}(X)$ with same acting group T. If the topological flow X is minimal, we can prove ${\tau}(X)$ is also minimal. The disjoint unions of the topological spaces can describe some topological systems (topological organisms). Here we will give a definition of topological organism. Our purpose of this study is to describe some properties concerning patterns of relationship between topology fields and topological organisms.

• Korean Journal of Mathematics
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• 제27권2호
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• pp.547-562
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• 2019

In this paper, we define a local topological group-groupoid and prove that if G is a local topological group-groupoid, then the monodromy groupoid Mon(G) of G is a local group-groupoid.

• 호남수학학술지
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• 제26권2호
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• pp.163-192
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• 2004

In this paper, we introduce the concepts of intuitionistic fuzzy subspaces, intuitionistic fuzzy topological groups and intuitionistic fuzzy quotient groups. And we investigate some of their properties.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제25권4호
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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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• 제8권2호
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• pp.103-110
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• 2000

We characterize some basic properties of fuzzy topological groups and semigroups and show that under some conditions in a fuzzy topological group G, $x{\in}\bar{A}$ iff $x{\cap}AU$ for any fuzzy subset A of G and the system {U} of all fuzzy open neighborhoods of the identity e such that $U(e)=1$.

• 충청수학회지
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• 제20권1호
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• pp.31-35
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• 2007

In dealing with transformation group, topological approach is very natural. But, it is not sufficient to investigate geometric properties of transformation group and we need geometric method. Frankel-McDuff Conjecture is very interesting in the point that it shows struggling between topological method and geometric method. In this paper, the author suggest generalized Frankel-McDuff conjecture as a topological version of the conjecture and construct a counterexample for the generalized version, and from this we assert that topological method does not work for Frankel-McDuff Conjecture.

• 대한수학회지
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• 제58권2호
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• pp.439-449
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• 2021

In this paper, we introduce the notions of expansiveness, shadowing property and topological stability for group actions on metric spaces and give a version of Walters's stability theorem for group actions on locally compact metric spaces. Moreover, we show that if G is a finitely generated virtually nilpotent group and there exists g ∈ G such that if Tg is expansive and has the shadowing property, then T is topologically stable.

• 대한수학회지
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• 제43권1호
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• pp.29-43
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• 2006

The article deals with the problem of extending representations of a closed normal subgroup H to a topological group G. We show that the standard technique using group cohomology to solve the problem in the case of finite groups can be generalized in the category of topological groups if G/H is discrete.

• Kyungpook Mathematical Journal
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• 제46권3호
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• pp.445-448
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• 2006

Let N be a normal subgroup of a path-connected topological group (G, $t$). In this paper, the authors consider the existence of path-connectedness in refined topologies in order to address the property of maximal path-connectedness in topological groups. In particular, refinements on $t$ and refinements on the quotient topology on G/N are studied. The preservation of path-connectedness in extending topologies and translation topologies is also considered.

• 대한수학회지
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• 제57권1호
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• pp.21-59
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• 2020

Let L_K denote the hypothetical automorphic Langlands group of a number field K. In our recent study, we briefly introduced a certain unconditional non-commutative topological group ${\mathfrak{W}}{\mathfrak{A}}{\frac{\varphi}{K}}$, called the Weil-Arthur idèle group of K, which, assuming the existence of L_K, comes equipped with a natural topological group homomorphism $NR{\frac{\varphi}{K}^{Langlands}}$ : ${\mathfrak{W}}{\mathfrak{A}}{\frac{\varphi}{K}}$ → L_K that we called the "Langlands form" of the global nonabelian norm-residue symbol of K. In this work, we present a detailed construction of ${\mathfrak{W}}{\mathfrak{A}}{\frac{\varphi}{K}}$ and $NR{\frac{\varphi}{K}^{Langlands}}$ : ${\mathfrak{W}}{\mathfrak{A}}{\frac{\varphi}{K}}$ → L_K, and discuss their basic properties.