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R-bipolar

  • R-bipolar #Card
    • Denoted by $R^{\circ\circ} A := (R^-)^\circ (R^\circ A)$. Properties: - $A_0 \subset A_1 \implies R^{\circ\circ} A_0 \subset R^{\circ\circ} A_1$ - $A \subset R^{\circ\circ} A$ - $R^{\circ\circ}(R^{\circ\circ} A) = R^{\circ\circ} A$

Back

Section titled “Back”

Denoted by $R^{\circ\circ} A := (R^-)^\circ (R^\circ A)$. Properties:

  • $A_0 \subset A_1 \implies R^{\circ\circ} A_0 \subset R^{\circ\circ} A_1$
  • $A \subset R^{\circ\circ} A$
  • $R^{\circ\circ}(R^{\circ\circ} A) = R^{\circ\circ} A$

Lean

Section titled “Lean”

本ノート RoyalRoad.ChapterI.bipolar と bipolar_extensive/bipolar_mono/bipolar_idem（閉包作用素）