1998 Fiscal Year Final Research Report Summary
Applications of Ramsey's theorem
| Project/Area Number |
09640249
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Yokohama National University |
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Principal Investigator |
TAMANO Kenichi Yokohama National University, Faculty of Engineering, professor, 工学部, 教授 (90171892)
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| Co-Investigator(Kenkyū-buntansha) |
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)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Ramsey's theorem / sequential fan / SIGMA-product / metrizability / graph / knot |
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| Research Abstract |
We got the following results concerning two purposes of our research.
(1) The sequential fan with kappa-many spines is the topological space obtained from the disjoint union of kappa-many 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 SIGMA-product 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 fan-tightness. 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 mu-space and by discussing various definitions of SIGMA-spaces.
(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.
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