Metamath Proof Explorer


Definition df-ldlf

Description: Definition of a Lindelöf space. A Lindelöf space is a topological space in which every open cover has a countable subcover. Definition 1 of BourbakiTop2 p. 195. (Contributed by Thierry Arnoux, 30-Jan-2020)

Ref Expression
Assertion df-ldlf
|- Ldlf = CovHasRef { x | x ~<_ _om }

Detailed syntax breakdown

Step Hyp Ref Expression
0 cldlf
 |-  Ldlf
1 vx
 |-  x
2 1 cv
 |-  x
3 cdom
 |-  ~<_
4 com
 |-  _om
5 2 4 3 wbr
 |-  x ~<_ _om
6 5 1 cab
 |-  { x | x ~<_ _om }
7 6 ccref
 |-  CovHasRef { x | x ~<_ _om }
8 0 7 wceq
 |-  Ldlf = CovHasRef { x | x ~<_ _om }