Clopen sandwiches

By dkl9, written 2024-149, revised 2024-149 (0 revisions)


An ordinary (closed) sandwich consists of two slices of bread with other food between them. For any one type of food, there is a natural amount, X, to pile on a slice of bread. A closed sandwich will hold either X of that food, or 2X, if you pile the inner ingredient on each side before closing it.

An open sandwich consists of one slice of bread, with food piled atop it, presumably in the same amount X, or slightly more.

You may want a high ratio of inner-ingredient-to-bread, especially if the inner ingredient is comparatively bland, or is a spread and so has relatively low X. Closed and open sandwiches each have at most X of their core ingredient per slice of bread. We can do better.

A sandwich both closed and open allows for 1.5X per slice. Borrowing the term from topology, I call them "clopen". To make a clopen sandwich, pile an inner ingredient on each of two slices of bread. Put the slices together as if making a closed sandwich. On the upward-exposed face of the bread, add more of the core ingredient.

A closed sandwich will stay closed iff you pinch it from both sides when holding it, or the food within is sticky, as with peanut butter, avocado, or some preparations of cheese. Typical sandwich ingredients can be messy. Their presence atop a clopen sandwich precludes pinching. The clopen sandwich method only works if at least some ingredients are sticky.