URYSOHN'S LEMMA IN SCHRÖDER CATEGORIES
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- 河原 康雄
- 九州大学システム情報科学研究院情報学部門
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説明
A Schröder category extends the category of all binary relations among sets, that is, it realises a relatively huge part of predicate logic. On the other hand Urysohn's lemma asserts that every pair of disjoint closed subsets in a $T_4$ topological space can be separated by a continuous function into the reals. Usually the lemma is demonstrated with calculus of elementary set theory. However the structure of this lemma is very interesting from a view point of lattice theory and relational method. This paper gives a relational proof for Urysohn's lemma within Schröder categories.
収録刊行物
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- Bulletin of informatics and cybernetics
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Bulletin of informatics and cybernetics 39 69-81, 2007-12
統計科学研究会
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詳細情報 詳細情報について
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- CRID
- 1390009224849127040
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- NII論文ID
- 120001944233
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- NII書誌ID
- AA10634475
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- DOI
- 10.5109/16775
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- ISSN
- 2435743X
- 0286522X
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- HANDLE
- 2324/16775
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- 本文言語コード
- en
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- 資料種別
- journal article
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- データソース種別
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- JaLC
- IRDB
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- CiNii Articles
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- 抄録ライセンスフラグ
- 使用可