Definition df-t1 21925

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

Step	Hyp	Ref	Expression
1		ct1 21918	. 2 class Fre
2		va	. . . . . . 7 setvar 𝑎
3	2	cv 1535	. . . . . 6 class 𝑎
4	3	csn 4570	. . . . 5 class {𝑎}
5		vx	. . . . . . 7 setvar 𝑥
6	5	cv 1535	. . . . . 6 class 𝑥
7		ccld 21627	. . . . . 6 class Clsd
8	6, 7	cfv 6358	. . . . 5 class (Clsd‘𝑥)
9	4, 8	wcel 2113	. . . 4 wff {𝑎} ∈ (Clsd‘𝑥)
10	6	cuni 4841	. . . 4 class ∪ 𝑥
11	9, 2, 10	wral 3141	. . 3 wff ∀𝑎 ∈ ∪ 𝑥{𝑎} ∈ (Clsd‘𝑥)
12		ctop 21504	. . 3 class Top
13	11, 5, 12	crab 3145	. 2 class {𝑥 ∈ Top ∣ ∀𝑎 ∈ ∪ 𝑥{𝑎} ∈ (Clsd‘𝑥)}
14	1, 13	wceq 1536	1 wff Fre = {𝑥 ∈ Top ∣ ∀𝑎 ∈ ∪ 𝑥{𝑎} ∈ (Clsd‘𝑥)}

This definition is referenced by:  ist1  21932