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Definition df-pnrm 17383
Description: Define perfectly normal spaces. A space is perfectly normal if it is normal and every closed set is a G&delta; set, meaning that it is a countable intersection of open sets. (Contributed by Mario Carneiro, 26-Aug-2015.)
Assertion
Ref Expression
df-pnrm  |- PNrm  =  {
j  e.  Nrm  | 
( Clsd `  j )  C_ 
ran  ( f  e.  ( j  ^m  NN )  |->  |^| ran  f ) }
Distinct variable group:    f, j

Detailed syntax breakdown of Definition df-pnrm
StepHypRef Expression
1 cpnrm 17376 . 2  class PNrm
2 vj . . . . . 6  set  j
32cv 1651 . . . . 5  class  j
4 ccld 17080 . . . . 5  class  Clsd
53, 4cfv 5454 . . . 4  class  ( Clsd `  j )
6 vf . . . . . 6  set  f
7 cn 10000 . . . . . . 7  class  NN
8 cmap 7018 . . . . . . 7  class  ^m
93, 7, 8co 6081 . . . . . 6  class  ( j  ^m  NN )
106cv 1651 . . . . . . . 8  class  f
1110crn 4879 . . . . . . 7  class  ran  f
1211cint 4050 . . . . . 6  class  |^| ran  f
136, 9, 12cmpt 4266 . . . . 5  class  ( f  e.  ( j  ^m  NN )  |->  |^| ran  f )
1413crn 4879 . . . 4  class  ran  (
f  e.  ( j  ^m  NN )  |->  |^|
ran  f )
155, 14wss 3320 . . 3  wff  ( Clsd `  j )  C_  ran  ( f  e.  ( j  ^m  NN ) 
|->  |^| ran  f )
16 cnrm 17374 . . 3  class  Nrm
1715, 2, 16crab 2709 . 2  class  { j  e.  Nrm  |  (
Clsd `  j )  C_ 
ran  ( f  e.  ( j  ^m  NN )  |->  |^| ran  f ) }
181, 17wceq 1652 1  wff PNrm  =  {
j  e.  Nrm  | 
( Clsd `  j )  C_ 
ran  ( f  e.  ( j  ^m  NN )  |->  |^| ran  f ) }
Colors of variables: wff set class
This definition is referenced by:  ispnrm  17403
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