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Definition df-t1 21041
Description: The class of all T1 spaces, also called Fréchet spaces. Morris, Topology without tears, p. 30 ex. 3. (Contributed by FL, 18-Jun-2007.)
Assertion
Ref Expression
df-t1 Fre = {𝑥 ∈ Top ∣ ∀𝑎 𝑥{𝑎} ∈ (Clsd‘𝑥)}
Distinct variable group:   𝑥,𝑎

Detailed syntax breakdown of Definition df-t1
StepHypRef Expression
1 ct1 21034 . 2 class Fre
2 va . . . . . . 7 setvar 𝑎
32cv 1479 . . . . . 6 class 𝑎
43csn 4153 . . . . 5 class {𝑎}
5 vx . . . . . . 7 setvar 𝑥
65cv 1479 . . . . . 6 class 𝑥
7 ccld 20743 . . . . . 6 class Clsd
86, 7cfv 5852 . . . . 5 class (Clsd‘𝑥)
94, 8wcel 1987 . . . 4 wff {𝑎} ∈ (Clsd‘𝑥)
106cuni 4407 . . . 4 class 𝑥
119, 2, 10wral 2907 . . 3 wff 𝑎 𝑥{𝑎} ∈ (Clsd‘𝑥)
12 ctop 20630 . . 3 class Top
1311, 5, 12crab 2911 . 2 class {𝑥 ∈ Top ∣ ∀𝑎 𝑥{𝑎} ∈ (Clsd‘𝑥)}
141, 13wceq 1480 1 wff Fre = {𝑥 ∈ Top ∣ ∀𝑎 𝑥{𝑎} ∈ (Clsd‘𝑥)}
Colors of variables: wff setvar class
This definition is referenced by:  ist1  21048
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