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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-bj-topmgmhom | Structured version Visualization version GIF version |
Description: Define the set of topological magma morphisms (continuous magma morphisms) between two topological magmas. If domain and codomain are topological semigroups, monoids, or groups, then one obtains the set of morphisms of these structures. This definition is currently stated with topological monoid domain and codomain, since topological magmas are currently not defined in set.mm. (Contributed by BJ, 10-Feb-2022.) |
Ref | Expression |
---|---|
df-bj-topmgmhom | ⊢ TopMgm⟶ = (𝑥 ∈ TopMnd, 𝑦 ∈ TopMnd ↦ ((𝑥 Top⟶ 𝑦) ∩ (𝑥 Mgm⟶ 𝑦))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ctopmgmhom 34448 | . 2 class TopMgm⟶ | |
2 | vx | . . 3 setvar 𝑥 | |
3 | vy | . . 3 setvar 𝑦 | |
4 | ctmd 22671 | . . 3 class TopMnd | |
5 | 2 | cv 1535 | . . . . 5 class 𝑥 |
6 | 3 | cv 1535 | . . . . 5 class 𝑦 |
7 | ctophom 34444 | . . . . 5 class Top⟶ | |
8 | 5, 6, 7 | co 7149 | . . . 4 class (𝑥 Top⟶ 𝑦) |
9 | cmgmhom 34446 | . . . . 5 class Mgm⟶ | |
10 | 5, 6, 9 | co 7149 | . . . 4 class (𝑥 Mgm⟶ 𝑦) |
11 | 8, 10 | cin 3928 | . . 3 class ((𝑥 Top⟶ 𝑦) ∩ (𝑥 Mgm⟶ 𝑦)) |
12 | 2, 3, 4, 4, 11 | cmpo 7151 | . 2 class (𝑥 ∈ TopMnd, 𝑦 ∈ TopMnd ↦ ((𝑥 Top⟶ 𝑦) ∩ (𝑥 Mgm⟶ 𝑦))) |
13 | 1, 12 | wceq 1536 | 1 wff TopMgm⟶ = (𝑥 ∈ TopMnd, 𝑦 ∈ TopMnd ↦ ((𝑥 Top⟶ 𝑦) ∩ (𝑥 Mgm⟶ 𝑦))) |
Colors of variables: wff setvar class |
This definition is referenced by: (None) |
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