22/01/15 00:14:53.83 E0wCw7+f.net
>>96 補足の補足
> １．普通に、添え字集合として、Vk k∈N （N＝{0,1,2,・・}（自然数））を考えて
> Vω=∪k=0～∞ Vk
> ↓
> Vω=∪k∈N Vk
> と解釈すれば良い
「∪k∈N Vk」のような記法は、普通に位相の開集合の公理でも出てくるよね（下記）
” {Ui:i∈ I}⊆ τ then ∪i∈I Ui∈ τ (any union of open sets is an open set)”などと
普通でしょ
(参考)
URLﾘﾝｸ(en.wikipedia.org)
Open set
Topological space
A topological space is a set on which a topology is defined, which consists of a collection of subsets that are said to be open, and satisfy the axioms given below.
More precisely, let X be a set. A family τ of subsets of X is a topology on X, and the elements of τ are the open sets of the topology if
・ X∈ τ and Φ ∈ τ (both X and Φ are open sets)
・ {Ui:i∈ I}⊆ τ then ∪i∈I Ui∈ τ (any union of open sets is an open set)
・ U1,・・・ ,Un∈ τ then U1∩ ・・・ ∩ Un∈ τ (any finite intersection of open sets is an open set)
Infinite intersections of open sets need not be open.
(引用終り)
以上