Lattice theory in the context of Power set

"Up tack" is the Unicode name for a symbol (⊥, \bot in LaTeX, U+22A5 in Unicode) that is also called "bottom", "falsum", "absurdum", or "absurdity", depending on context. It is used to represent:

• The truth value 'false', or a logical constant denoting a proposition in logic that is always false. (The names "falsum", "absurdum" and "absurdity" come from this context.)
• The bottom element in wheel theory and lattice theory, which also represents absurdum when used for logical semantics
• The bottom type in type theory, which is the bottom element in the subtype relation. This may coincide with the empty type, which represents absurdum under the Curry–Howard correspondence
• The "undefined value" in quantum physics interpretations that reject counterfactual definiteness, as in (r₀,⊥)

Garrett Birkhoff (January 19, 1911 – November 22, 1996) was an American mathematician. He is best known for his work in lattice theory and Universal Algebra.

The mathematician George Birkhoff (1884–1944) was his father.

In mathematics, a filter or order filter is a special subset of a partially ordered set (poset), describing "large" or "eventual" elements. Filters appear in order and lattice theory, but also topology, whence they originate. The notion dual to a filter is an order ideal.

Special cases of filters include ultrafilters, which are filters that cannot be enlarged, and describe nonconstructive techniques in mathematical logic.

Mathematical morphology (MM) is a theory and technique for the analysis and processing of geometrical structures, based on set theory, lattice theory, topology, and random functions. MM is most commonly applied to digital images, but it can be employed as well on graphs, surface meshes, solids, and many other spatial structures.

Topological and geometrical continuous-space concepts such as size, shape, convexity, connectivity, and geodesic distance, were introduced by MM on both continuous and discrete spaces. MM is also the foundation of morphological image processing, which consists of a set of operators that transform images according to the above characterizations.