Priestley Sketchpad figure

Examples

Settings

Close the order: add the relations a closed order forces at limits (if every x_n ≤ p, then x_∞ ≤ p) Show tail dots and fading edges into the tail Shade the up-set and down-set of the clicked element Mark the localic points: those x whose principal down-set ↓x is clopen Snap to the grid (hold Alt to place freely)

How to draw

Point P: Click to place a point.
Relation R: Click the smaller element, then the larger. Shift-click a term to use its whole sequence.
Repeat N: Select points or βℕ copies, press Repeat, then click where the copies go: up for an increasing chain, down for a decreasing one, sideways for an antichain. Relations among them repeat termwise. Then compactify: one point, or Stone–Čech.
Space: Inserts a Priestley space drawn as a region: the Cantor space, its Gleason cover, or one whose properties you set. Duplicate it for a copy that can lie pointwise below or above it.
Select V: Click to edit it in the panel on the left, drag to move. The clicked element’s up-set is shaded green, its down-set orange.
Sequences: Drag a term to move just that term. Shift-click or Shift-drag a box to pick several terms and drag them together. Double-click a term to select the whole sequence and drag it all.
Copy: Shift-click or Shift-drag to select several things, then Ctrl+C and Ctrl+V. Ctrl+D duplicates, Ctrl+A selects everything.

Only covering relations are drawn, larger elements higher up. The panel on the right is about the whole space: the checks, its properties and what they mean for the dual lattice.

Clicking a term relates

Sketchpad

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