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In mathematics, a cofinite subset of a set is a subset whose complement in is a finite set. In other words, contains all but finitely many elements of If the complement is not finite, but it is countable, then one says the set is cocountable. These arise naturally when generalizing structures on finite sets to infinite sets, particularly on infinite products, as in the or . This use of the prefix "co" to describe a property possessed by a set's complement is consistent with its use in other terms such as "comeagre set".

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  • Topologia cofinita (ca)
  • Kofinite Topologie (de)
  • Topología cofinita (es)
  • Cofiniteness (en)
  • Topologia cofinita (it)
  • Topologie cofinie (fr)
  • 쌍대 유한 집합 (ko)
  • 補有限 (ja)
  • 餘有限空間 (zh)
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  • En matemàtiques, la topologia dels complementaris finits o topologia cofinita sobre un conjunt és la topologia definida per És a dir, un subconjunt de és obert si el seu complementari és un conjunt finit. (ca)
  • In mathematics, a cofinite subset of a set is a subset whose complement in is a finite set. In other words, contains all but finitely many elements of If the complement is not finite, but it is countable, then one says the set is cocountable. These arise naturally when generalizing structures on finite sets to infinite sets, particularly on infinite products, as in the or . This use of the prefix "co" to describe a property possessed by a set's complement is consistent with its use in other terms such as "comeagre set". (en)
  • Im mathematischen Teilgebiet der Topologie bezeichnet die kofinite Topologie (auch cofinite Topologie geschrieben) eine Klasse pathologischer Beispiele für topologische Räume. Sie lässt sich über einer beliebigen Menge definieren: In ihr sind genau die Mengen offen, deren Komplemente endlich oder die selbst leer sind. Dies ist äquivalent dazu, dass die abgeschlossenen Mengen genau die endlichen Mengen oder die ganze Menge sind. Im Folgenden betrachten wir die kofinite Topologie nur über unendlichen Mengen, da sie interessante Eigenschaften tragen (im endlichen Fall erhält man die diskrete Topologie). (de)
  • En matemáticas, la topología de los complementos finitos o topología cofinita sobre un conjunto es la topología dada por Es decir, un subconjunto de es abierto si su complemento es un conjunto finito. (es)
  • La topologie cofinie est la topologie que l'on peut définir sur tout ensemble X de la manière suivante : l'ensemble des ouverts est constitué de l'ensemble vide et parties de X cofinies, c'est-à-dire dont le complémentaire dans X est fini. Formellement, si l'on note τ la topologie cofinie sur X, on a : ou plus simplement, en définissant la topologie via les fermés : les fermés de X sont X et ses parties finies. (fr)
  • La topologia cofinita su un insieme X è la topologia i cui chiusi sono tutti e soli i sottoinsiemi finiti, oltre a X stesso. Un sottoinsieme cofinito di un insieme X è un sottoinsieme A di X che contiene tutti gli elementi di X tranne un numero finito di essi. In altri termini, il suo complemento in X è un insieme finito. Questa topologia è la meno fine fra tutte quelle che soddisfano l'assioma T1 di separabilità; in altre parole, è la meno fine fra tutte quelle in cui ciascun punto costituisce un insieme chiuso. (it)
  • 집합론에서 쌍대 유한 집합(雙對有限集合, 영어: cofinite set) 그 여집합이 유한 집합인 부분 집합이다. (ko)
  • 数学において、集合 X の部分集合 A が補有限（ほゆうげん、英: cofinite; 余有限）であるとは、A の X における補集合が有限集合であることをいう。すなわち、補有限集合 A は「 X の有限個の例外を除く全ての元を含む」ような X の部分集合である。補集合が有限でなく可算である場合、その集合は（あるいは余可算）であるという。 補有限の概念は、有限集合に関するものを無限集合に対して一般化する際に自然に生ずる。特に、直積位相や直和加群などのような無限積について、無限であるのと補有限であるのとで本質的な差異を生むものもある。 (ja)
  • 若給定一個集合，為的子集，使得差集為有限集合，則稱為的餘有限集（cofinite）。 類似地，若給定一個集合，為的子集，使得差集為可數集，則稱為餘可數集（cocountable）。 上述的東西都是一些很自然地推廣，當我們開始從有限集合進入到無限集合時。 (zh)
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