Project/Area Number  09640249 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
General mathematics (including Probability theory/Statistical mathematics)

Research Institution  Yokohama National University 
Principal Investigator 
TAMANO Kenichi Yokohama National University, Faculty of Engineering, professor, 工学部, 教授 (90171892)

CoInvestigator(Kenkyūbuntansha) 
NISHIMURA Takashi Yokohama National University, Faculty of Education and Human Sciences, associate, 教育人間科学部, 助教授 (80189307)
NEGAMI Seiya Yokohama National University, Faculty of Education and Human Sciences, associate, 教育人間科学部, 助教授 (40164652)
HIRANO Norimichi Yokohama National University, Faculty of Engineering, professor, 工学研究科, 教授 (80134815)
TERADA Toshiji Yokohama National University, Faculty of Engineering, professor, 工学研究科, 教授 (80126383)

Project Fiscal Year 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥2,400,000 (Direct Cost : ¥2,400,000)
Fiscal Year 1998 : ¥1,000,000 (Direct Cost : ¥1,000,000)
Fiscal Year 1997 : ¥1,400,000 (Direct Cost : ¥1,400,000)

Keywords  Ramsey's theorem / sequential fan / SIGMAproduct / metrizability / graph / knot / ラムゼイ / 点列ファン / シグマ積 / 距離化可能 / グラフ / 結び目 / 正規 / M_3空間 / 位相空間論 / 距離化定理 
Research Abstract 
We got the following results concerning two purposes of our research. (1) The sequential fan with kappamany spines is the topological space obtained from the disjoint union of kappamany convergent sequences by identifying all the limit point to a single point. One of the purposes of our research was to study Kodama's question on the normality of SIGMAproduct of sequential fans by using Ramsey type combinatorics. Tamano and Feng proved that a subspace of a countable product of sequential fans (more generally, Lasnev spaces) is metrizable if and only if it has countable fantightness. The class of Lasnev spaces is a kind of generalized metric spaces. We contributed to the theory of generalized metric spaces by showing the existence of a space with a countable network which is not a muspace and by discussing various definitions of SIGMAspaces. (2) An embedding of a graph into R^3 is called a spatial embedding of the graph. It had been known that a sufficently large complete graph always include a nonsplittable link and a nontrivial knot, which is a kind of Ramsey type theorem. Negami proved that such a theorem holds for an embedding called good drawing.
