• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제3권2호
• /
• pp.131-139
• /
• 1996

Topos is a set-like category. For an axiom of choice in a topos, F. W. Lawvere and A. M. Penk introduced another versions of the axiom of choice. Also it is showed that general axiom of choice and Penk's axiom of choice are weaker than Lawvere's axiom of choice. In this paper we study that weak form of axiom of choice, axiom of choice, Penk's axiom of choice and Lawvere's axiom of choice are all equivalent in a well pointed topos.

• 대한수학회논문집
• /
• 제19권1호
• /
• pp.29-34
• /
• 2004

There are various forms of the axiom of choice and also various weak forms of the axiom of choice in a topos. This paper give equivalent forms of the axiom of choice in a well-pointed topos.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제15권1호
• /
• pp.85-92
• /
• 2008

In topoi, there are various forms of the axiom of choice such as (ES), (AC) and (WO). And also there are various weak forms of the axiom of choice such as (DES), (IAC) and (ASC). First we investigate the relation between (IAC) and (ASC), and then we study the relation between (AC) and (WO). We get equivalent forms of the axiom of choice in a well-pointed topos.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제13권4호
• /
• pp.249-254
• /
• 2006

Category Fuz of fuzzy sets has a similar function to the topos Set. But Category Fuz forms a weak topos. We show that supports split weakly(SSW) and with some properties, implicity axiom of choice(IAC) holds in weak topos Fuz. So weak axiom of choice(WAC) holds in weak topos Fuz. Also we show that weak extensionality principle for arrow holds in weak topos Fuz.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제10권3호
• /
• pp.171-176
• /
• 2003

The purpose of this paper is to Show the relationships between three forms of the axiom of choice and well-ordering in an elementary topos.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제2권1호
• /
• pp.25-29
• /
• 1995

The topos constructed in [6] is a set-like category that includes among its axioms an axiom of infinity and an axiom of choice. In its final form a topos is free from any such axioms. Set$\^$G/ is a topos whose object are G-set Ψ$\sub$s/:G${\times}$S\longrightarrowS and morphism f:S \longrightarrowT is an equivariants map. We already known that Set$\^$G/ satisfies the weak form of the axiom of choice but it does not satisfies the axiom of the choice.(omitted)

• 충청수학회지
• /
• 제16권2호
• /
• pp.75-78
• /
• 2003

The Tychonoff product theorem is one of the most fundamental theorems in general topology. As is well-known, the proof of the Tychonoff product theorem relies on the axiom of choice. The converse was also conjectured by S. Kakutani and Kelley [1] then resolved this conjecture in his historical short note on 1950. However, the original proof due to Kelley has a flaw. According to this observation, we provide a correction of the proof in this paper.

• 대한수학회논문집
• /
• 제21권2호
• /
• pp.211-217
• /
• 2006

Topos is a set-like category. In topos, the axiom of choice can be expressed as (AC1), (AC2) and (AC3). Category Fuz of fuzzy sets has a similar function to the topos Set and it forms weak topos. But Fuz does not satisfy (AC1), (AC2) and (AC3). So we define (WAC1), (WAC2) and (WAC3) in weak topos Fuz. And we show that they are equivalent in Fuz.

• 한국수학사학회지
• /
• 제22권4호
• /
• pp.115-128
• /
• 2009

본 논문에서 von Neumann의 공리계를 수정하여 새로운 DVN공리계를 소개한다. 그리고 DVN공리계에서 불가지 류의 존재성을 조사하고, 불가지류와 선택공리의 관계를 논한다.

• 한국수학사학회지
• /
• 제9권2호
• /
• pp.1-9
• /
• 1996

This paper is a sequel to [26]. We investigate how the Axiom of Choice has been accepted after Zermelo introduced the Axiom in 1904. The response to the Axiom has divided into two groups of mathematicians, namely idealists and empiricists. We also investigate how the Zorn's lemma (1935) has been emerged. It was originally formulated by Hausdorff in 1909 and then by many other mathematicians independently.