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In mathematics, a hereditary property is a property of an object, that inherits to all its ''subobjects'', where the term subobject depends on the context. These properties are particularly considered in topology and graph theory, but also in set theory. ==In topology== In topology, a topological property is said to be ''hereditary'' if whenever a topological space has that property, then so does every subspace of it. If the latter is true only for closed subspaces, then the property is called ''weakly hereditary''. For example, second countability and metrisability are hereditary properties. Sequentiality and Hausdorff compactness are weakly hereditary, but not hereditary.〔 *Goreham, Anthony, "(Sequential Convergence in Topological Spaces )〕 Connectivity is not weakly hereditary. If ''P'' is a property of a topological space ''X'' and every subspace also has property ''P'', then ''X'' is said to be "hereditarily ''P''". 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「hereditary property」の詳細全文を読む スポンサード リンク
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