TAKEUCHI Gaishi Mathematician 1926-2017
From Author;
This translation has several ambiguity by automatism.
So sorry.
Original text is Japanese.
TAKEUCHI Gaishi sent me the Road to Meaning through mathematics
What is set? 1976
Published by Kodansha as a book of Blue Bucks in 1976
This book explains the most basic concept of set in mathematics from Cantor, which was the starting point, to the latest in modern set theory in a very easy-to-understand manner. However, it may be necessary to annotate the expression that it is easy to understand .
As a second high school language teacher, I spent three years from 1976 to 1978 at Tokyo Metropolitan Ome Higashi High School in Ome City, Tokyo, where I met a young math teacher. He taught mathematics as a lecturer at Tokyo University of Science after completing a master’s course, but felt the limits of his abilities and chose to start again as a high school teacher and was assigned to Ome Higashi High School. He was thinking of taking a PhD at Kyoto University if he had the ability, but he told me that he hadn’t had the ability to do so. In such a story, when I told him about Gaisi Takeuti’s book, it seemed interesting, so he asked me to study together, so in my spare time after school, the blackboard In a room, he became a teacher and I became a student, and from the beginning of the book, the two of us examined the potential problems one by one.
One of the hearts of this book was to describe how the numbers 1-9 are generated by set theory. I couldn’t understand some of them by myself, so I asked him, a teacher with a blackboard on his back. After thinking for a while, he tried to write the solution on the blackboard, but he ran around and replied, “I don’t know this.” I couldn’t have understood that he was a university lecturer. He said it was “difficult” and the study of the day was over, which was the final study session of this set theory.
Since then, I have talked with him on various topics. He was always polite because I was a little older. He didn’t break his stance when I told him to speak more normally. In March 1979, I changed from the same school to a part-time job at Tokyo Metropolitan Agricultural High School in Fuchu City, and from April I became a major student in Wako during the daytime. He was soon transferred to Tokyo Metropolitan High School, one of the leading colleges in Hachioji, and one night he met him by train for the first time in a while. He asked me about the situation in the language department of the national university and told him what I knew. He certainly thought I would continue to study the language.
TANAKA Akio
1 December 2024
Tokyo
Sekinan Hills
is supposed.
V (k) \ D,
and there becomes 
are different reduced divisors each other over V.
.
each other,
is finite subset.
is regular cut to D.
is approximate function to D.
is counting function to D.
is rich line bundle.
islarge, 
becomes rich.
is basis of 
.
is embedding.
,
,
.
\ 
is 
integer under the next condition.
.
\ 
.
\ 
[x1, x2, ..., xn]
Cn f (a1, a2, ..., an) = 0, 
a }
Rf
.
)-1U)
is surjection, t
.
p
is dominant.
satisfies next conditions is called algebraic variety.
I, intersection 
is open partia; set of 
.
that defines surjective homomorphism is expressed by 
.
of closed embedding defined by 
is called glue of A and B by C.
Spm R, Spm T 
Spm S
, next is equivalent.
is generated by R and S.
is called R value point of X.
X(S)
is function from ring category over k to category of set.
over ring R {
}
satisfies the next conditions, 
.
,
is existent uniquely.
k, 
(k') is always bijection.
is functor to group's category is called algebraic group.
are commutative for 
.
for A.
{
}
.
is called closed map when 
is closed set image 
becomes closed set.
is closed map for arbitrary manifold Y.
is closed map.