Question: Information: - Mathematics (from Greek "mathma", knowledge, study, learning) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics. - Category theory formalizes mathematical structure and its concepts in terms of a collection of "objects" and of "arrows" (also called morphisms). A category has two basic properties: the ability to compose the arrows associatively and the existence of an identity arrow for each object. The language of category theory has been used to formalize concepts of other high-level abstractions such as sets, rings, and groups. - In combinatorics, a greedoid is a type of set system. It arises from the notion of the matroid, which was originally introduced by Whitney in 1935 to study planar graphs and was later used by Edmonds to characterize a class of optimization problems that can be solved by greedy algorithms. Around 1980, Korte and Lovasz introduced the greedoid to further generalize this characterization of greedy algorithms; hence the name greedoid. Besides mathematical optimization, greedoids have also been connected to graph theory, language theory, poset theory, and other areas of mathematics. - A definition is a statement of the meaning of a term (a word, phrase, or other set of symbols). Definitions can be classified into two large categories, intensional definitions (which try to give the essence of a term) and extensional definitions (which proceed by listing the objects that a term describes). Another important category of definitions is the class of ostensive definitions, which convey the meaning of a term by pointing out examples. A term may have many different senses and multiple meanings, and thus require multiple definitions. - In mathematics , a simplicial complex is a topological space of a certain kind , constructed by the union of points , line segments , triangles , and their n - dimensional counterparts ( see illustration ) . Simplicial complexes should not be confused with the more abstract notion of a simplicial set appearing in modern simplicial homotopy theory . The purely combinatorial counterpart to a simplicial complex is an abstract simplicial complex . - In mathematics, higher category theory is the part of category theory at a "higher order", which means that some equalities are replaced by explicit arrows in order to be able to explicitly study the structure behind those equalities. - In combinatorics, a branch of mathematics, a matroid is a structure that abstracts and generalizes the notion of linear independence in vector spaces. There are many equivalent ways to define a matroid, the most significant being in terms of independent sets, bases, circuits, closed sets or flats, closure operators, and rank functions. - Quantity is a property that can exist as a magnitude or multitude. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value in terms of a unit of measurement. Quantity is among the basic classes of things along with quality, substance, change, and relation. Some quantities are such by their inner nature (as number), while others are functioning as states (properties, dimensions, attributes) of things such as heavy and light, long and short, broad and narrow, small and great, or much and little. A small quantity is sometimes referred to as a quantulum. - In mathematics, a simplicial set is a construction in categorical homotopy theory that is a pure algebraic model of the notion of a "well-behaved" topological space. Historically, this model arose from earlier work in combinatorial topology and in particular from the notion of simplicial complexes. Simplicial sets are used to define quasi-categories, a basic notion of higher category theory. - In mathematics, an abstract simplicial complex is a purely combinatorial description of the geometric notion of a simplicial complex, consisting of a family of non-empty finite sets closed under the operation of taking non-empty subsets. In the context of matroids and greedoids, abstract simplicial complexes are also called independence systems. - In mathematics, a finite set is a set that has a finite number of elements. For example, is a finite set with five elements. The number of elements of a finite set is a natural number (a non-negative integer) and is called the cardinality of the set. A set that is not finite is called infinite. For example, the set of all positive integers is infinite: Finite sets are particularly important in combinatorics, the mathematical study of counting. Many arguments involving finite sets rely on the pigeonhole principle, which states that there cannot exist an injective function from a larger finite set to a smaller finite set. - In mathematics, especially in set theory, a set "A" is a subset of a set "B", or equivalently "B" is a superset of "A", if "A" is "contained" inside "B", that is, all elements of "A" are also elements of "B". "A" and "B" may coincide. The relationship of one set being a subset of another is called inclusion or sometimes containment. - Space is the boundless three-dimensional extent in which objects and events have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum known as spacetime. The concept of space is considered to be of fundamental importance to an understanding of the physical universe. However, disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a conceptual framework. - In mathematics, combinatorial topology was an older name for algebraic topology, dating from the time when topological invariants of spaces (for example the Betti numbers) were regarded as derived from combinatorial decompositions of spaces, such as decomposition into simplicial complexes . After the proof of the simplicial approximation theorem this approach provided rigour. Given the information above, choose from the list below the object entity that exhibits the relation 'subclass of' with the subject 'simplicial complex'. Choices: - being - branch - category - change - closure - concept - construction - decomposition - definition - description - direction - essence - family - finite set - graph theory - greek - illustration - injective function - knowledge - language - learning - line - magnitude - mathematical optimization - mathematical structure - mathematics - model - name - natural - object - operation - out - principle - property - quantity - rank - set - set theory - space - statement - structure - theory - topological space - topology - type - unit of measurement - word - work
Answer:
mathematical structure