Mathbox for Thierry Arnoux |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > ordtconn | Structured version Visualization version GIF version |
Description: Connectedness in the order topology of a complete uniform totally ordered space. (Contributed by Thierry Arnoux, 15-Sep-2018.) |
Ref | Expression |
---|---|
ordtconn.x | ⊢ 𝐵 = (Base‘𝐾) |
ordtconn.l | ⊢ ≤ = ((le‘𝐾) ∩ (𝐵 × 𝐵)) |
ordtconn.j | ⊢ 𝐽 = (ordTop‘ ≤ ) |
Ref | Expression |
---|---|
ordtconn | ⊢ ⊤ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tru 1543 | 1 ⊢ ⊤ |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1539 ⊤wtru 1540 ∩ cin 3885 × cxp 5582 ‘cfv 6426 Basecbs 16922 lecple 16979 ordTopcordt 17220 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 206 df-tru 1542 |
This theorem is referenced by: (None) |
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