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・ Hereditary multiple exostoses
・ Hereditary neuralgic amyotrophy
・ Hereditary neuropathy with liability to pressure palsy
・ Hereditary nonpolyposis colorectal cancer
・ Hereditary officers of the Roman Curia
・ Hereditary Order of Descendants of Colonial Governors
・ Hereditary pancreatitis
・ Hereditary peer
・ Hereditary Peerage Association
・ Hereditary persistence of fetal hemoglobin
・ Hereditary politicians
・ Hereditary Prince of Monaco
・ Hereditary Princes of Modena
・ Hereditary Princesses of Modena
・ Hereditary progressive mucinous histiocytosis
Hereditary property
・ Hereditary pyropoikilocytosis
・ Hereditary Quartermaster General of the Sacred Apostolic Palace
・ Hereditary Revenues Act 1856
・ Hereditary ring
・ Hereditary sclerosing poikiloderma
・ Hereditary sensory and autonomic neuropathy
・ Hereditary sensory and autonomic neuropathy type I
・ Hereditary set
・ Hereditary spastic paraplegia
・ Hereditary spherocytosis
・ Hereditary stomatocytosis
・ Hereditary title
・ Hereditary witch
・ Hereditas


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Hereditary property : ウィキペディア英語版
Hereditary property
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)
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