Perfect space as alias for P132 (#790)

properties/P000132.md

@@ -1,16 +1,20 @@
 ---
 uid: P000132
 name: $G_\delta$ space
+aliases:
+ - Perfect
 refs:
  - doi: 10.1007/978-1-4612-6290-9
  name: Counterexamples in Topology
  - wikipedia: Gδ_space
  name: G-delta space
+ - zb: "0684.54001"
+ name: General Topology (Engelking, 1989)
 ---
 
-A space in which every closed set is a $G_\delta$ (a countable intersection of open sets).
-Equivalently, a space in which every open set is an $F_\sigma$ (a countable union of closed sets).
+A space in which every closed set is a $G_\delta$ set (a countable intersection of open sets).
+Equivalently, a space in which every open set is an $F_\sigma$ set (a countable union of closed sets).
 
 Defined on page 162 of {{doi:10.1007/978-1-4612-6290-9}}.
 
-Note: A $G_\delta$ space is sometimes called a "perfect space" (Exercise 1.5.H(a) in {{zb:0684.54001}}). But that could be confused with a space that is a "perfect" in the sense of "perfect set" (= a set equal to its derived set), that is, a space without isolated point. See the discussion in <https://en.wikipedia.org/wiki/Talk:Perfect_set#Terminology_issue>.
+Note: A $G_\delta$ space is sometimes called a "perfect space" (Exercise 1.5.H(a) in {{zb:0684.54001}}). Not to be be confused with a space that is a "perfect" in the sense of "perfect set" (= a set equal to its derived set = a closed set that is dense-in-itself), that is, a space without isolated point. See the discussion in <https://en.wikipedia.org/wiki/Talk:Perfect_set#Terminology_issue>.