ConstructionConstruction is a general term meaning the art and science to form objects, systems, or organizations, and comes from Latin constructio (from com- "together" and struere "to pile up") and Old French construction. To construct is the verb: the act of building, and the noun is construction: how something is built, the nature of its structure. In its most widely used context, construction covers the processes involved in delivering buildings, infrastructure, industrial facilities, and associated activities through to the end of their life.
Construction managementConstruction management (CM) is a professional service that uses specialized, project management techniques and software to oversee the planning, design, construction and closeout of a project. The purpose of construction management is to control the quality of a project's scope, time / delivery and cost—sometimes referred to as a project management triangle or "triple constraints." CM is compatible with all project delivery systems, including design-bid-build, design-build, CM At-Risk and Public Private Partnerships.
Construction engineeringConstruction engineering, also known as construction operations, is a professional subdiscipline of civil engineering that deals with the designing, planning, construction, and operations management of infrastructure such as roadways, tunnels, bridges, airports, railroads, facilities, buildings, dams, utilities and other projects. Construction engineers learn some of the design aspects similar to civil engineers as well as project management aspects.
Homotopy groupIn mathematics, homotopy groups are used in algebraic topology to classify topological spaces. The first and simplest homotopy group is the fundamental group, denoted which records information about loops in a space. Intuitively, homotopy groups record information about the basic shape, or holes, of a topological space. To define the n-th homotopy group, the base-point-preserving maps from an n-dimensional sphere (with base point) into a given space (with base point) are collected into equivalence classes, called homotopy classes.
Homotopy theoryIn mathematics, homotopy theory is a systematic study of situations in which maps can come with homotopies between them. It originated as a topic in algebraic topology but nowadays is studied as an independent discipline. Besides algebraic topology, the theory has also been used in other areas of mathematics such as algebraic geometry (e.g., A1 homotopy theory) and (specifically the study of ). In homotopy theory and algebraic topology, the word "space" denotes a topological space.
Outline of constructionThe following outline is provided as an overview of and topical guide to construction: Construction – process of building or assembling infrastructure. A complex activity, large scale construction involves extensive multitasking. Normally, a job is managed by a project manager, and supervised by a construction manager, design engineer, construction engineer or project architect. Building Planning permission Nonbuilding structures including infrastructure Building construction Home construction High-rise co
Homotopy categoryIn mathematics, the homotopy category is a built from the category of topological spaces which in a sense identifies two spaces that have the same shape. The phrase is in fact used for two different (but related) categories, as discussed below. More generally, instead of starting with the category of topological spaces, one may start with any and define its associated homotopy category, with a construction introduced by Quillen in 1967. In this way, homotopy theory can be applied to many other categories in geometry and algebra.
Homotopy fiberIn mathematics, especially homotopy theory, the homotopy fiber (sometimes called the mapping fiber) is part of a construction that associates a fibration to an arbitrary continuous function of topological spaces . It acts as a homotopy theoretic kernel of a mapping of topological spaces due to the fact it yields a long exact sequence of homotopy groupsMoreover, the homotopy fiber can be found in other contexts, such as homological algebra, where the distinguished trianglegives a long exact sequence analogous to the long exact sequence of homotopy groups.
Covering spaceA covering of a topological space is a continuous map with special properties. Let be a topological space. A covering of is a continuous map such that there exists a discrete space and for every an open neighborhood , such that and is a homeomorphism for every . Often, the notion of a covering is used for the covering space as well as for the map . The open sets are called sheets, which are uniquely determined up to a homeomorphism if is connected. For each the discrete subset is called the fiber of .
Homotopy groups of spheresIn the mathematical field of algebraic topology, the homotopy groups of spheres describe how spheres of various dimensions can wrap around each other. They are examples of topological invariants, which reflect, in algebraic terms, the structure of spheres viewed as topological spaces, forgetting about their precise geometry. Unlike homology groups, which are also topological invariants, the homotopy groups are surprisingly complex and difficult to compute.
HomotopyIn topology, a branch of mathematics, two continuous functions from one topological space to another are called homotopic (from ὁμός "same, similar" and τόπος "place") if one can be "continuously deformed" into the other, such a deformation being called a homotopy (həˈmɒtəpiː, ; ˈhoʊmoʊˌtoʊpiː, ) between the two functions. A notable use of homotopy is the definition of homotopy groups and cohomotopy groups, important invariants in algebraic topology. In practice, there are technical difficulties in using homotopies with certain spaces.
Weak equivalence (homotopy theory)In mathematics, a weak equivalence is a notion from homotopy theory that in some sense identifies objects that have the same "shape". This notion is formalized in the axiomatic definition of a . A model category is a with classes of morphisms called weak equivalences, fibrations, and cofibrations, satisfying several axioms. The associated of a model category has the same objects, but the morphisms are changed in order to make the weak equivalences into isomorphisms.
Covering groupIn mathematics, a covering group of a topological group H is a covering space G of H such that G is a topological group and the covering map p : G → H is a continuous group homomorphism. The map p is called the covering homomorphism. A frequently occurring case is a double covering group, a topological double cover in which H has index 2 in G; examples include the spin groups, pin groups, and metaplectic groups.
Path (topology)In mathematics, a path in a topological space is a continuous function from the closed unit interval into Paths play an important role in the fields of topology and mathematical analysis. For example, a topological space for which there exists a path connecting any two points is said to be path-connected. Any space may be broken up into path-connected components. The set of path-connected components of a space is often denoted One can also define paths and loops in pointed spaces, which are important in homotopy theory.
Locally connected spaceIn topology and other branches of mathematics, a topological space X is locally connected if every point admits a neighbourhood basis consisting entirely of open, connected sets. Throughout the history of topology, connectedness and compactness have been two of the most widely studied topological properties. Indeed, the study of these properties even among subsets of Euclidean space, and the recognition of their independence from the particular form of the Euclidean metric, played a large role in clarifying the notion of a topological property and thus a topological space.
Optical coatingAn optical coating is one or more thin layers of material deposited on an optical component such as a lens, prism or mirror, which alters the way in which the optic reflects and transmits light. These coatings have become a key technology in the field of optics. One type of optical coating is an anti-reflective coating, which reduces unwanted reflections from surfaces, and is commonly used on spectacle and camera lenses. Another type is the high-reflector coating, which can be used to produce mirrors that reflect greater than 99.
Locally simply connected spaceIn mathematics, a locally simply connected space is a topological space that admits a basis of simply connected sets. Every locally simply connected space is also locally path-connected and locally connected. The circle is an example of a locally simply connected space which is not simply connected. The Hawaiian earring is a space which is neither locally simply connected nor simply connected. The cone on the Hawaiian earring is contractible and therefore simply connected, but still not locally simply connected.
Anti-reflective coatingAn antireflective, antiglare or anti-reflection (AR) coating is a type of optical coating applied to the surface of lenses, other optical elements, and photovoltaic cells to reduce reflection. In typical imaging systems, this improves the efficiency since less light is lost due to reflection. In complex systems such as cameras, binoculars, telescopes, and microscopes the reduction in reflections also improves the contrast of the image by elimination of stray light. This is especially important in planetary astronomy.
Glossary of topologyThis is a glossary of some terms used in the branch of mathematics known as topology. Although there is no absolute distinction between different areas of topology, the focus here is on general topology. The following definitions are also fundamental to algebraic topology, differential topology and geometric topology. All spaces in this glossary are assumed to be topological spaces unless stated otherwise. Absolutely closed See H-closed Accessible See . Accumulation point See limit point.
Topological propertyIn topology and related areas of mathematics, a topological property or topological invariant is a property of a topological space that is invariant under homeomorphisms. Alternatively, a topological property is a proper class of topological spaces which is closed under homeomorphisms. That is, a property of spaces is a topological property if whenever a space X possesses that property every space homeomorphic to X possesses that property. Informally, a topological property is a property of the space that can be expressed using open sets.
