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Definition df-conn 21196
Description: Topologies are connected when only and 𝑗 are both open and closed. (Contributed by FL, 17-Nov-2008.)
Assertion
Ref Expression
df-conn Conn = {𝑗 ∈ Top ∣ (𝑗 ∩ (Clsd‘𝑗)) = {∅, 𝑗}}

Detailed syntax breakdown of Definition df-conn
StepHypRef Expression
1 cconn 21195 . 2 class Conn
2 vj . . . . . 6 setvar 𝑗
32cv 1480 . . . . 5 class 𝑗
4 ccld 20801 . . . . . 6 class Clsd
53, 4cfv 5876 . . . . 5 class (Clsd‘𝑗)
63, 5cin 3566 . . . 4 class (𝑗 ∩ (Clsd‘𝑗))
7 c0 3907 . . . . 5 class
83cuni 4427 . . . . 5 class 𝑗
97, 8cpr 4170 . . . 4 class {∅, 𝑗}
106, 9wceq 1481 . . 3 wff (𝑗 ∩ (Clsd‘𝑗)) = {∅, 𝑗}
11 ctop 20679 . . 3 class Top
1210, 2, 11crab 2913 . 2 class {𝑗 ∈ Top ∣ (𝑗 ∩ (Clsd‘𝑗)) = {∅, 𝑗}}
131, 12wceq 1481 1 wff Conn = {𝑗 ∈ Top ∣ (𝑗 ∩ (Clsd‘𝑗)) = {∅, 𝑗}}
Colors of variables: wff setvar class
This definition is referenced by:  isconn  21197
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