• Language and Information
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• v.13 no.1
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• pp.21-38
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• 2009

Since countability is a grammatical notion, the distinction between count and mass nouns may not reflect countability in the real world. Based on this, Chierchia (1998a; 1998b) provides a typological study of plurality and genericity, which does not account for countability in Korean. Nemoto (2005) revises Chierchia's analysis to deal with count and mass nouns in Korean and Japanese. This study discusses problems with the previous analyses and proposes that the semantic feature of humanness is the main criterion for countability in Korean.

• Journal of the Korean Institute of Intelligent Systems
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• v.13 no.1
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• pp.114-118
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• 2003

We study some relations between separability in fuzzy topological spaces and one in fuzzy hyperspaces. And we investigate some properties of axiom of countability in fuzzy hyperspaces.

• 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 $pMET^{\infty}$.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.12a
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• pp.67-70
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• 2002

We study some relations between separability in fuzzy topological spaces and one in fuzzy hyperspaces. And we investigate some properties of axiom of countability in fuzzy hyperspaces.

• The Pure and Applied Mathematics
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• v.11 no.3
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• pp.243-265
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• 2004

In this paper, we introduce the fundamental concepts of intuitionistic fuzzy Q-neighborhood, intuitionistic Q-first axiom of countability, intuitionistic first axiom of countability, intuitionistic fuzzy closure operator, intuitionistic fuzzy boundary point and intuitionistic fuzzy accumulation point and investigate some of their properties.

• East Asian mathematical journal
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• v.7 no.2
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• pp.165-170
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• 1992

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1299-1307
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• 2023

In this paper, we attempt to study several topological properties for the function space H(X), space of self-homeomorphisms on a metric space endowed with the regular topology. We investigate its metrizability and countability and prove their coincidence at X compact. Furthermore, we prove that the space H(X) endowed with the regular topology is a topological group when X is a metric, almost P-space. Moreover, we prove that the homeomorphism spaces of increasing and decreasing functions on ℝ under regular topology are open subspaces of H(ℝ) and are homeomorphic.

• Communications of Mathematical Education
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• v.22 no.4
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• pp.471-487
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• 2008

Inventive mathematical thinking, original mathematical problem solving ability, mathematical invention and so on are core concepts, which must be emphasized in all branches of mathematical education. In particular, Polya(1981) insisted that inventive thinking must be emphasized in a suitable level of university mathematical courses. In this paper, the author considered two cases of inventive problem solving ability shown by his many students via real analysis courses. The first case is about the proof of the problem "what is the derived set of the integers Z?" Nearly all books on mathematical analysis sent the question without the proof but some books said that the answer is "empty". Only one book written by Noh, Y. S.(2006) showed the proof by using the definition of accumulation points. But the proof process has some mistakes. But our student Kang, D. S. showed the perfect proof by using The Completeness Axiom, which is very useful in mathematical analysis. The second case is to show the infinite countability of NxN, which is shown by informal proof in many mathematical analysis books with formal proofs. Some students who argued the informal proof as an unreasonable proof were asked to join with us in finding the one-to-one correspondences between NxN and N. Many students worked hard and find two singled-valued mappings and one set-valued mapping covering eight diagrams in the paper. The problems are not easy and the proofs are a little complicated. All the proofs shown in this paper are original and right, so the proofs are deserving of inventive mathematical thoughts, original mathematical problem solving abilities and mathematical inventions. From the inventive proofs of his students, the author confirmed that any students can develope their mathematical abilities by their professors' encouragements.