• Journal of the Korean Mathematical Society
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• v.59 no.2
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• pp.367-377
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• 2022

Let G be a non-discrete locally compact abelian group, and 𝜇 be a transformable and translation bounded Radon measure on G. In this paper, we construct a Segal algebra S_𝜇(G) in L¹(G) such that the generalized Poisson summation formula for 𝜇 holds for all f ∈ S_𝜇(G), for all x ∈ G. For the definitions of transformable and translation bounded Radon measures and the generalized Poisson summation formula, we refer to L. Argabright and J. Gil de Lamadrid's monograph in 1974.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.883-894
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• 2021

The aim of this work is to introduce for the first time the concept of D-set. This is done by defining a special type of cover called a D-cover. we present some results to study the properties of D-compact spaces and their relations with other topological spaces. Several examples are discussed to illustrate and support our main results. Our results extend and generalized many will known results in the literature.

• Communications of the Korean Mathematical Society
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• v.24 no.2
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• pp.277-280
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• 2009

In this paper, we prove the following two statements: (1) There exists a Hausdorff locally $Lindel{\ddot{o}}f$ centered-$Lindel{\ddot{o}}f$ space that is not star-$Lindel{\ddot{o}}f$. (2) There exists a $T_1$ locally compact centered-$Lindel{\ddot{o}}f$ space that is not star-$Lindel{\ddot{o}}f$. The two statements give a partial answer to Bonanzinga and Matveev [2, Question 1].

• Communications of the Korean Mathematical Society
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• v.20 no.1
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• pp.79-92
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• 2005

It is shown that the K-theory of the $C^{\ast}$-algebras of continuous fields on locally compact Hausdorff spaces with fibers elementary $C^{\ast}$-algebras is the same as the K-theory of the base spaces. We also consider the slightly generalized case. Furthermore, we give some applications of these results.

• Journal of applied mathematics & informatics
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• v.38 no.3_4
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• pp.249-254
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• 2020

Here, assume that X is a compact space. we show that if f is a locally nonexpansive map then f : X → X has the limit shadowing property if and only if f : CR(f) → CR(f) has the limit shadowing property. Also we prove that if f is a local expansion then f has the limit shadowing property.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.585-602
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• 2019

We characterize Gelfand-continuous functions from a Tychonoff space X into an Arens-Michael algebra A. Then we define several algebras of such functions, and investigate them as topological algebras. Finally, we provide a class of examples of (metrizable) commutative unital complete Arens-Michael algebras A and locally compact spaces X for which all these algebras differ from each other.

• 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.

• Journal of the Korean Mathematical Society
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• v.47 no.2
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• pp.299-309
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• 2010

The Weyl group of a compact connected Lie group is a reflection group. If such Lie groups are locally isomorphic, the representations of the Weyl groups are rationally equivalent. They need not however be equivalent as integral representations. Turning to the invariant theory, the rational cohomology of a classifying space is a ring of invariants, which is a polynomial ring. In the modular case, we will ask if rings of invariants are polynomial algebras, and if each of them can be realized as the mod p cohomology of a space, particularly for dihedral groups.

• Kyungpook Mathematical Journal
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• v.28 no.1
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• pp.79-82
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• 1988

This paper investigates the relationship between compactness and pseudo-compactness in subsets of C(X) where X is locally compact and first countable. Two primary theorems are proven. First, equicontinuity at a point is proven to be equivalent to the existence of a certain open cover of a pseudo-compact subset of C(X). The second theorem proves the equivalence of compactness and pseudo-compctness for closed subsets F of C(X).

• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.337-344
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• 2018

We extend Bowen's decomposition theorem to topologically Anosov homeomorphisms on first countable, locally compact, paracompact, Hausdorff spaces which are not necessarily metrizable and not necessarily compact.