Connected spaceIn topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint non-empty open subsets. Connectedness is one of the principal topological properties that are used to distinguish topological spaces. A subset of a topological space is a if it is a connected space when viewed as a subspace of . Some related but stronger conditions are path connected, simply connected, and -connected.
Domain (mathematical analysis)In mathematical analysis, a domain or region is a non-empty connected open set in a topological space, in particular any non-empty connected open subset of the real coordinate space Rn or the complex coordinate space Cn. A connected open subset of coordinate space is frequently used for the domain of a function, but in general, functions may be defined on sets that are not topological spaces.
Simply connected spaceIn topology, a topological space is called simply connected (or 1-connected, or 1-simply connected) if it is path-connected and every path between two points can be continuously transformed (intuitively for embedded spaces, staying within the space) into any other such path while preserving the two endpoints in question. The fundamental group of a topological space is an indicator of the failure for the space to be simply connected: a path-connected topological space is simply connected if and only if its fundamental group is trivial.
Domain of a functionIn mathematics, the domain of a function is the set of inputs accepted by the function. It is sometimes denoted by or , where f is the function. In layman's terms, the domain of a function can generally be thought of as "what x can be". More precisely, given a function , the domain of f is X. In modern mathematical language, the domain is part of the definition of a function rather than a property of it. In the special case that X and Y are both subsets of , the function f can be graphed in the Cartesian coordinate system.
22 (two) is a number, numeral and digit. It is the natural number following 1 and preceding 3. It is the smallest and only even prime number. Because it forms the basis of a duality, it has religious and spiritual significance in many cultures. The digit used in the modern Western world to represent the number 2 traces its roots back to the Indic Brahmic script, where "2" was written as two horizontal lines. The modern Chinese and Japanese languages (and Korean Hanja) still use this method.
Cauchy sequenceIn mathematics, a Cauchy sequence, named after Augustin-Louis Cauchy, is a sequence whose elements become arbitrarily close to each other as the sequence progresses. More precisely, given any small positive distance, all but a finite number of elements of the sequence are less than that given distance from each other. It is not sufficient for each term to become arbitrarily close to the term. For instance, in the sequence of square roots of natural numbers: the consecutive terms become arbitrarily close to each other – their differences tend to zero as the index n grows.
Akkadian languageAkkadian (əˈkeɪdiən; Akkadian: ) is an extinct East Semitic language that was spoken in ancient Mesopotamia (Akkad, Assyria, Isin, Larsa, Babylonia and perhaps Dilmun) from the third millennium BC until its gradual replacement in common use by Old Aramaic among Assyrians and Babylonians from the 8th century BC. It is the earliest documented Semitic language. It used the cuneiform script, which was originally used to write the unrelated, and also extinct, Sumerian (which is a language isolate), as well as the fellow East Semitic language Eblaite, the Hurro-Urartian language Hurrian, Elamite (another language isolate) and the Indo-European language Hittite.
Sumerian languageSumerian (Cuneiform: "native tongue") is the language of ancient Sumer. It is one of the oldest attested languages, dating back to at least 2900 BC. It is accepted to be a local language isolate and to have been spoken in ancient Mesopotamia, in the area that is modern-day Iraq. Akkadian, a Semitic language, gradually replaced Sumerian as a spoken language in the area 2000 BC (the exact date is debated), but Sumerian continued to be used as a sacred, ceremonial, literary and scientific language in Akkadian-speaking Mesopotamian states such as Assyria and Babylonia until the 1st century AD.
