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Mirrors > Home > MPE Home > Th. List > df-cnp | Structured version Visualization version Unicode version |
Description: Define a function on two topologies whose value is the set of continuous mappings at a specified point in the first topology. Based on Theorem 7.2(g) of [Munkres] p. 107. (Contributed by NM, 17-Oct-2006.) |
Ref | Expression |
---|---|
df-cnp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ccnp 21029 | . 2 | |
2 | vj | . . 3 | |
3 | vk | . . 3 | |
4 | ctop 20698 | . . 3 | |
5 | vx | . . . 4 | |
6 | 2 | cv 1482 | . . . . 5 |
7 | 6 | cuni 4436 | . . . 4 |
8 | 5 | cv 1482 | . . . . . . . . 9 |
9 | vf | . . . . . . . . . 10 | |
10 | 9 | cv 1482 | . . . . . . . . 9 |
11 | 8, 10 | cfv 5888 | . . . . . . . 8 |
12 | vy | . . . . . . . . 9 | |
13 | 12 | cv 1482 | . . . . . . . 8 |
14 | 11, 13 | wcel 1990 | . . . . . . 7 |
15 | vg | . . . . . . . . . 10 | |
16 | 5, 15 | wel 1991 | . . . . . . . . 9 |
17 | 15 | cv 1482 | . . . . . . . . . . 11 |
18 | 10, 17 | cima 5117 | . . . . . . . . . 10 |
19 | 18, 13 | wss 3574 | . . . . . . . . 9 |
20 | 16, 19 | wa 384 | . . . . . . . 8 |
21 | 20, 15, 6 | wrex 2913 | . . . . . . 7 |
22 | 14, 21 | wi 4 | . . . . . 6 |
23 | 3 | cv 1482 | . . . . . 6 |
24 | 22, 12, 23 | wral 2912 | . . . . 5 |
25 | 23 | cuni 4436 | . . . . . 6 |
26 | cmap 7857 | . . . . . 6 | |
27 | 25, 7, 26 | co 6650 | . . . . 5 |
28 | 24, 9, 27 | crab 2916 | . . . 4 |
29 | 5, 7, 28 | cmpt 4729 | . . 3 |
30 | 2, 3, 4, 4, 29 | cmpt2 6652 | . 2 |
31 | 1, 30 | wceq 1483 | 1 |
Colors of variables: wff setvar class |
This definition is referenced by: cnpfval 21038 iscnp2 21043 |
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