翻訳と辞書 Words near each other ・ Dense connective tissue ・ Dense granule ・ Dense graph ・ Dense heterarchy ・ Dense Inert Metal Explosive ・ Dense irregular connective tissue ・ Dense non-aqueous phase liquid ・ Dense order ・ Dense Pack ・ Dense plasma focus ・ Dense regular connective tissue ・ Dense set ・ Dense subgraph ・ Dense submodule ・ Dense Time ・ Dense-in-itself ・ Dense-rock equivalent ・ Dense-scale lantern shark ・ Denseisha ・ Densely defined operator ・ Densely packed decimal ・ Densen Audio Technologies ・ Densen Uta ・ Densetsu no Shōjo ・ Densetsu no Stafy (video game) ・ Densetsu no Stafy 2 ・ Densetsu no Stafy 3 ・ Densetsu no Stafy 4 ・ Densey Clyne ・ Densha de Go! Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Dense-in-itself ： ウィキペディア英語版 Dense-in-itself In mathematics, a subset $A$ of a topological space is said to be dense-in-itself if $A$ contains no isolated points. Every dense-in-itself closed set is perfect. Conversely, every perfect set is dense-in-itself. A simple example of a set which is dense-in-itself but not closed (and hence not a perfect set) is the subset of irrational numbers (considered as a subset of the real numbers). This set is dense-in-itself because every neighborhood of an irrational number $x$ contains at least one other irrational number $y\; \backslash neq\; x$. On the other hand, this set of irrationals is not closed because every rational number lies in its closure. For similar reasons, the set of rational numbers (also considered as a subset of the real numbers) is also dense-in-itself but not closed. The above examples, the irrationals and the rationals, are also dense sets in their topological space, namely $\backslash mathbb$. As an example that is dense-in-itself but not dense in its topological space, consider $\backslash mathbb\; \backslash cap\; ()$. This set is not dense in $\backslash mathbb$ but is dense-in-itself. ==See also== * Nowhere dense set * Dense order * Perfect space * Glossary of topology 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Dense-in-itself」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.