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; the terms you click set the index shift, so Shift-clicking p₁ then q₀ relates p_n+1 ≤ q_n for every n.

Repeat N

Select points or βℕ copies, press Repeat, then click where the copies go: up for increasing chains, down for decreasing ones, sideways for an antichain. Each point becomes its own chain; hold Shift while clicking to stack the copies instead, each wholly below (or above) the next. Copies of βℕ always go side by side, with no order between them. Relations among them repeat termwise. Then compactify: one point, or Stone–Čech. Select one convergent sequence instead for a sequence of sequences: each copy keeps its own limit, and One point adds a limit of the copies.

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. Click an edge to select the relations it comes from. 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.

Play A

Watch the diagram build itself: points and sequences appear one by one, each limit after its terms, each edge once both its ends are there. A relation that closedness forces flashes once it is drawn. Space pauses, ← → or the slider go back and forward, the speed button switches between 1×, 2× and ½×, and Esc or a click on the drawing shows the finished diagram. Nothing is changed or checked while it plays.

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.