21/06/16 07:32:59.45 gpkuWhQq.net
>>49-50
The ordinal α is compact as a topological space if and only if α is a successor ordinal.
順序数αが(順序)位相空間としてコンパクトであるのは、αが後続順序数であるとき、そのときに限る
(引用終り)
おサルさ、文章を一部だけ切り取ってくるのは、なんだかね
あと、出典を明示しないとね
上記は、複数検索ヒットするが、下記が代表例でしょう
下記の“Ordinals as topological spaces”の項にある
残念ながら、（よくあることだが）日本語のwikipediaページはない
URLﾘﾝｸ(en.wikipedia.org)
Order topology
In mathematics, an order topology is a certain topology that can be defined on any totally ordered set. It is a natural generalization of the topology of the real numbers to arbitrary totally ordered sets.
A topological space X is called orderable if there exists a total order on its elements such that the order topology induced by that order and the given topology on X coincide. The order topology makes X into a completely normal Hausdorff space.
The standard topologies on R, Q, Z, and N are the order topologies.
つづく