Description: The discrete topology on a set A expressed as a topological space. (Contributed by FL, 20-Aug-2006)
Ref | Expression | ||
---|---|---|---|
Hypotheses | distps.a | |- A e. _V |
|
distps.k | |- K = { <. ( Base ` ndx ) , A >. , <. ( TopSet ` ndx ) , ~P A >. } |
||
Assertion | distps | |- K e. TopSp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | distps.a | |- A e. _V |
|
2 | distps.k | |- K = { <. ( Base ` ndx ) , A >. , <. ( TopSet ` ndx ) , ~P A >. } |
|
3 | unipw | |- U. ~P A = A |
|
4 | 3 | eqcomi | |- A = U. ~P A |
5 | distop | |- ( A e. _V -> ~P A e. Top ) |
|
6 | 1 5 | ax-mp | |- ~P A e. Top |
7 | 2 4 6 | eltpsi | |- K e. TopSp |