# compactness

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**Totally bounded space**— In topology and related branches of mathematics, a totally bounded space is a space that can be covered by finitely many subsets of any fixed size (where the meaning of size depends on the given context). The smaller the size fixed, the more… …52

**Pseudocompact space**— In mathematics, in the field of topology, a topological space is said to be pseudocompact if its image under any continuous function to R is bounded.Conditions for pseudocompactness*Every countably compact space is pseudocompact. For normal… …53

**Particular point topology**— In mathematics, the particular point topology (or included point topology) is a topology where sets are considered open if they are empty or contain a particular, arbitrarily chosen, point of the topological space. Formally, let X be any set and… …54

**Protein domain**— Pyruvate kinase, a protein from three domains (PDB 1pkn) A protein domain is a part of protein sequence and structure that can evolve, function, and exist independently of the rest of the protein chain. Each domain forms a compact three… …55

**topology**— topologic /top euh loj ik/, topological, adj. topologically, adv. topologist, n. /teuh pol euh jee/, n., pl. topologies for 3. Math. 1. the study of those properties of geometric forms that remain invariant under c …56

**Non-standard model of arithmetic**— In mathematical logic, a nonstandard model of arithmetic is a model of (first order) Peano arithmetic that contains nonstandard numbers. The standard model of arithmetic consists of the set of standard natural numbers {0, 1, 2, …}. The elements… …57

**Algorithm**— Flow chart of an algorithm (Euclid s algorithm) for calculating the greatest common divisor (g.c.d.) of two numbers a and b in locations named A and B. The algorithm proceeds by successive subtractions in two loops: IF the test B ≤ A yields yes… …58

**Net (mathematics)**— This article is about nets in topological spaces and not about ε nets in other fields. In mathematics, more specifically in general topology and related branches, a net or Moore–Smith sequence is a generalization of the notion of a sequence. In… …59

**Regular expression**— In computing, a regular expression provides a concise and flexible means for matching (specifying and recognizing) strings of text, such as particular characters, words, or patterns of characters. Abbreviations for regular expression include… …60

**Shape of the Universe**— Edge of the Universe redirects here. For the Bee Gees song, see Edge of the Universe (song). The local geometry of the universe is determined by whether Omega is less than, equal to or greater than 1. From top to bottom: a spherical universe, a… …