Set-thoretic approach to the extension problem of continuous functions in topology
| Project/Area Number |
22540123
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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 | Shizuoka University |
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Principal Investigator |
OHTA Haruto 静岡大学, 教育学部, 教授 (40126769)
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| Co-Investigator(Renkei-kenkyūsha) |
YAMADA Kohzo 静岡大学, 教育学部, 教授 (00200717)
TAMANO Ken-ichi 横浜国立大学, 大学院工学研究院, 教授 (90171892)
YAMAZAKI Kaori 高崎経済大学, 経済学部, 教授 (80301076)
YORIOKA Teruyuki 静岡大学, 理学研究科, 准教授 (60432192)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 位相空間 / トポロジー / 連続関数 / 拡張問題 / 集合論 / Dowker 空間 / 連続写像 / 正規空間 / 初等的部分モデル / Dowker空間 |
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| Research Abstract |
The purpose of this research is to apply recent results of set-theory to the extension problem of a continuous function or a family of continuous functions on a topological space. In particular, we analyze the construction of Dowker spaces by Z. Balogh, which is one of key words in the problem. We give a combinatorial proof without using elementary submodels that Balogh's natural Dowker space is not countably paracompact (H. Ohta-T. Yorioka, 2012). Moreover, as by-products, we prove that every dense-in-itself separable metric space has an independent subbase (H. Ohta-H. Tsuiki-S. Yamada).
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Report
(5 results)
Research Products
(16 results)
