드 모르간 틀

이승온 한국수학사학회 2004 Journal for history of mathematics Vol.17 No.2

Stone introduced extremally disconnected spaces as the image of complete Boolean algebras under his famous duality between Bool and ZComp and they turn out to be projective objects in various categories of Hausdorff spaces and completely regular ones are exactly those X with Dedekind complete C(X, ). In the pointfree setting, extremally disconnected frame (= De Morgan frame) are those with De Morgan condition. In this paper, we investigate a historical aspect of De Morgan frame together with that of De Morgan. 스톤은 스톤 쌍대성에 의하여 완비 불 대수는 극단적으로 비연결인 콤팩트 하우스도르프 공간에 대응되어 불 대수의 범주 Bool에서 단사 대상은 완비 불 대수인 사실에 의하여 0차원 콤팩트 공간의 범주 ZComp의 사영 대상은 극단적으로 비연결인 콤팩트 공간임을 증명하였고, 완전 정규 공간 X가 극단적인 비연결 공간이기 위한 필요충분조건은 X에서 실직선로의 연속함수의 순서집합 C(X, )이 데데킨트 완비인 사실[6]이 드모르간 틀에서도 성립함을 증명하였다[2]. 이 논문에서는 드 모르간의 역사를 조사하고, 드모르간 틀을 도입하여 극단적인 비연결 공간과의 관계와 드 모르간 틀과 불 대수 사이의 관계를 연구한다.

고른 구조의 역사

이승온,민병수 한국수학사학회 2004 Journal for history of mathematics Vol.17 No.3

해석학에서는 위상 구조와 고른 구조를 거리 공간에서 다루었기 때문에 많은 혼동이 있었다. 거리 공간의 개념은 위상 구조로 일반화되었지만 '고르다'는 개념은 그 후에 앙드레 베이유에 의해서 고른 구조로 일반화되었다. 우리는 먼저 베이유의 삶과 그의 수학적 업적을 살피고 고른 구조의 역사와 발달에 대해서 알아볼 것이다. In the Analysis, there have been many cases of confusion on topological structure and uniform structure because they were dealt in metric spaces. The concept of metric spaces is generalized into that of topological spaces but its uniform aspect was much later generalized into the uniform structure by A. Weil. We first investigate Weil's life and his mathematical achievement and then study the history of the uniform structure and its development.

fuzzy(r)-preopen sets

이승온,이은표 한국지능시스템학회 2005 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.5 No.2

In this paper, we introduce the concepts of fuzzy -preopen sets and fuzzy -precontinuous mappings on intuitionistic fuzzy topological spaces in Sostak's sense and then we investigate some of their characteristic properties.

서양 수학사와 종교

이승온 충북대학교 과학교육연구소 1997 과학교육연구논총 Vol.13 No.1

Religion is a specific set of beliefs and practices usually involving devotional and ritual observances. Thus, it often contains a moral code for the conduct of human affairs. On the contrary, mathematics can be defined as a systematic treatment of relationships between figures, forms, and quantities. Unlike religion that resorts to an emotional or irrational aspect of human mind, mathematics is a rational discipline. Surprisingly, these two old and seemingly antithetical human inquiries have been closely related to each other ever since the beginning stage of their development. In ancient times, especially before the end of Western Roman Empire (A. D. 476), mathematics was a discipline indistinguishable from the Christian religion. In the Middle Ages (from about A. D. 476 to the Renaissance), the development of the mathematical approach was feasible only in the religious context of the times. It could be said that virtually no progress was made during this period. It was after the Middle Ages that mathematics could become an independent discipline free from the impact of religion. In this paper, I examine and evaluate the degree to which religion has impinged upon the developmental process of mathematics.

Stably 가산 근사 Frames와 Strongly Lindelof Frames

이승온 한국수학사학회 2003 Journal for history of mathematics Vol.16 No.1

This paper is a sequel to [11]. We introduce $\sigma$-coherent frames, stably countably approximating frames and strongly Lindelof frames, and show that a stably countably approximating frame is a strongly Lindelof frame. We also show that a complete chain in a Lindelof frame if and only if it is a strongly Lindelof frame by using the concept of strong convergence of filters. Finally, using the concepts of super compact frames and filter compact frames, we introduce an example of a strongly Lindelof frame which is not a stably countably approximating frame.

고대와 중세의 서양 논리사

이승온,정창훈,이석종 한국수학사학회 1997 Journal for history of mathematics Vol.10 No.1

In this paper, we investigate a relation between the history of western logic and religion. Logic, as distinct from theology, began in Greece in the sixth century B. C. After running its course in antiquity, it was again submerged by theology as Christianity rose and Rome fell. Its second great period, from the eleventh to the fourteenth centuries, was dominated by the Catholic church, except for a few great rebels, such as the Emperor Frederick II(1195-1250). This period was brought to an end by the confusion that culminated in the Reformation. The third period, from the seventeenth century to the present day is dominated by science; traditional religious beliefs remain important but are felt to need justification, and are modified wherever science seems to make this imperative.

On Atomic Lattices

이승온,연용호,황인재,Lee, Seung-On,Yon, Yong-Ho,Hwang, In-Jae 한국수학사학회 2006 Journal for history of mathematics Vol.19 No.4

격자의 기원은 수학에서 비롯된 것이 아니고 논리학에서 시작되었다([22]). 1880 년경 Peirce는 모든 격자는 분배 격자라고 생각하였으나 1890년경 $Schr{\"{o}}der$가 오류를 수정하였고, 1933년 Birkhoff가 lattice라는 단어를 처음 사용하였으나 이는 오늘의 격자와는 그 정의가 다르다. 이 논문에서는 Peirce를 소개하고 atomic 격자, atomistic 격자, J-격자, strong 격자 그리고 분배 격자의 상관관계를 연구한다. The lattice originated from logic, not mathematics. Around 1880, Peirce thought that all the lattices were distributives, however $Schr{\"{o}}der$ corrected the error around 1890. In 1993, Birkhoff used the term lattice for the first time that had a different meaning from today's lattice. This paper introduces Peirce, and studies correlation among atomic lattices, atomistic lattices, J-lattices, strong lattices and distributive lattices.

퍼지 논리의 시조 Zadeh

이승온,김진태,Lee, Seung-On,Kim, Jin-Tae 한국수학사학회 2008 Journal for history of mathematics Vol.21 No.1

퍼지 논리는 1965년 Zadeh([13])에 의하여 소개된 이후 꾸준히 확장, 발전하였다. 퍼지 논리와 관련된 수학사 및 수학교육 논문([1], [2], [3], [4], [5], [7])들이 많이 발표되었지만 정작 퍼지 논리의 창시자인 Zadeh에 대한 연구 논문은 아직 발표되지 않았다. 본 논문에서는 Zadeh의 생애와 업적을 알아보고 이를 통해 우리가 배워야 할 점들에 대해 논의한다. 또한 이가 논리, 다가 논리, 퍼지 논리, 직관주의 논리 및 직관적 퍼지 집합을 비교, 분석하고 직관적 퍼지 집합에서 '직관적(intuitionistic)' 이라는 용어의 부적절성에 대해 논의한다. Fuzzy logic is introduced by Zadeh in 1965. It has been continuously developed by many mathematicians and knowledge engineers all over the world. A lot of papers concerning with the history of mathematics and the mathematical education related with fuzzy logic, but there is no paper concerning with Zadeh. In this article, we investigate his life and papers about fuzzy logic. We also compare two-valued logic, three-valued logic, fuzzy logic, intuisionistic logic and intuitionistic fuzzy sets. Finally we discuss about the expression of intuitionistic fuzzy sets.

Fuzzy pairwise (r, s)-irresolute mappings

이승온,이은표 한국지능시스템학회 2009 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.9 No.2

In this paper, we introduce the concepts of fuzzy pairwise (r, s)-irresolute, fuzzy pairwise (r, s)-presemiopen and fuzzy pairwise (r, s)-presemiclosed mappings in smooth bitopological spaces and then we investigate some of their characteristic properties.

DEGREE OF NEARNESS

이승온,이은표 충청수학회 2008 충청수학회지 Vol.21 No.2

This paper is a revised version of [5]. In [5], we define ’nearness between two points’ in a topological space in many ways and show that a continuous function preserves one-sided nearness. We also show that a T1-space is characterized by one-sided nearness exactly. In this paper, we introduce extremally disconnected paces and show that the new topology generated by the set of equivalence classes as a base is extremally disconnected.