Complex projective spaceIn mathematics, complex projective space is the projective space with respect to the field of complex numbers. By analogy, whereas the points of a real projective space label the lines through the origin of a real Euclidean space, the points of a complex projective space label the complex lines through the origin of a complex Euclidean space (see below for an intuitive account). Formally, a complex projective space is the space of complex lines through the origin of an (n+1)-dimensional complex vector space.
Housing associationIn Ireland and the United Kingdom, housing associations are private, non-profit making organisations that provide low-cost "social housing" for people in need of a home. Any budget surplus is used to maintain existing housing and to help finance new homes and it cannot be used for personal benefit of directors or shareholders. Although independent, they are regulated by the state and commonly receive public funding. They are now the United Kingdom's major providers of new housing for rent, while many also run shared ownership schemes to help those who cannot afford to buy a home outright.
Urban renewalUrban renewal (also called urban regeneration in the United Kingdom and urban redevelopment in the United States) is a program of land redevelopment often used to address urban decay in cities. Urban renewal involves the clearing out of blighted areas in inner cities to clear out slums and create opportunities for higher class housing, businesses, and other developments. A primary purpose of urban renewal is to restore economic viability to a given area by attracting external private and public investment and by encouraging business start-ups and survival.
Complex geometryIn mathematics, complex geometry is the study of geometric structures and constructions arising out of, or described by, the complex numbers. In particular, complex geometry is concerned with the study of spaces such as complex manifolds and complex algebraic varieties, functions of several complex variables, and holomorphic constructions such as holomorphic vector bundles and coherent sheaves. Application of transcendental methods to algebraic geometry falls in this category, together with more geometric aspects of complex analysis.
Complex torusIn mathematics, a complex torus is a particular kind of complex manifold M whose underlying smooth manifold is a torus in the usual sense (i.e. the cartesian product of some number N circles). Here N must be the even number 2n, where n is the complex dimension of M. All such complex structures can be obtained as follows: take a lattice Λ in a vector space V isomorphic to Cn considered as real vector space; then the quotient group is a compact complex manifold. All complex tori, up to isomorphism, are obtained in this way.
Projective varietyIn algebraic geometry, a projective variety over an algebraically closed field k is a subset of some projective n-space over k that is the zero-locus of some finite family of homogeneous polynomials of n + 1 variables with coefficients in k, that generate a prime ideal, the defining ideal of the variety. Equivalently, an algebraic variety is projective if it can be embedded as a Zariski closed subvariety of .
Big-box storeA big-box store (also hyperstore, supercenter, superstore, or megastore) is a physically large retail establishment, usually part of a chain of stores. The term sometimes also refers, by extension, to the company that operates the store. The term "big-box" references the typical appearance of buildings occupied by such stores. Commercially, big-box stores can be broken down into two categories: general merchandise (examples include Walmart, Target, and Kmart), and specialty stores (such as The Home Depot, Barnes & Noble, or Best Buy), which specialize in goods within a specific range, such as hardware, books, or consumer electronics, respectively.
Complex manifoldIn differential geometry and complex geometry, a complex manifold is a manifold with an atlas of charts to the open unit disc in , such that the transition maps are holomorphic. The term complex manifold is variously used to mean a complex manifold in the sense above (which can be specified as an integrable complex manifold), and an almost complex manifold. Since holomorphic functions are much more rigid than smooth functions, the theories of smooth and complex manifolds have very different flavors: compact complex manifolds are much closer to algebraic varieties than to differentiable manifolds.
Public housing in the United KingdomPublic housing in the United Kingdom, also known as council housing or social housing, provided the majority of rented accommodation until 2011 when the number of households in private rental housing surpassed the number in social housing. Dwellings built for public or social housing use are built by or for local authorities and known as council houses. Since the 1980s non-profit housing associations became more important and subsequently the term "social housing" became widely used, as technically council housing only refers to housing owned by a local authority, though the terms are largely used interchangeably.
Scale (map)The scale of a map is the ratio of a distance on the map to the corresponding distance on the ground. This simple concept is complicated by the curvature of the Earth's surface, which forces scale to vary across a map. Because of this variation, the concept of scale becomes meaningful in two distinct ways. The first way is the ratio of the size of the generating globe to the size of the Earth. The generating globe is a conceptual model to which the Earth is shrunk and from which the map is projected.
