Nerve (category theory)In , a discipline within mathematics, the nerve N(C) of a C is a simplicial set constructed from the objects and morphisms of C. The geometric realization of this simplicial set is a topological space, called the classifying space of the category C. These closely related objects can provide information about some familiar and useful categories using algebraic topology, most often homotopy theory. The nerve of a category is often used to construct topological versions of moduli spaces.
Group isomorphismIn abstract algebra, a group isomorphism is a function between two groups that sets up a one-to-one correspondence between the elements of the groups in a way that respects the given group operations. If there exists an isomorphism between two groups, then the groups are called isomorphic. From the standpoint of group theory, isomorphic groups have the same properties and need not be distinguished.
Wi-FiWi-Fi (ˈwaɪfaɪ) is a family of wireless network protocols based on the IEEE 802.11 family of standards, which are commonly used for local area networking of devices and Internet access, allowing nearby digital devices to exchange data by radio waves. These are the most widely used computer networks in the world, used globally in home and small office networks to link devices together and to a wireless router to connect them to the Internet, and in wireless access points in public places like coffee shops, hotels, libraries, and airports to provide visitors with Internet connectivity for their mobile devices.
Railroad switchA railroad switch ( ()), turnout, or [set of] points ( ()) is a mechanical installation enabling railway trains to be guided from one track to another, such as at a railway junction or where a spur or siding branches off. The most common type of switch consists of a pair of linked tapering rails, known as points (switch rails or point blades), lying between the diverging outer rails (the stock rails). These points can be moved laterally into one of two positions to direct a train coming from the point blades toward the straight path or the diverging path.
Li-FiLi-Fi (also written as LiFi) is a wireless communication technology which utilizes light to transmit data and position between devices. The term was first introduced by Harald Haas during a 2011 TEDGlobal talk in Edinburgh. Li-Fi is a light communication system that is capable of transmitting data at high speeds over the visible light, ultraviolet, and infrared spectrums. In its present state, only LED lamps can be used for the transmission of data in visible light.
CommutingCommuting is periodically recurring travel between one's place of residence and place of work or study, where the traveler, referred to as a commuter, leaves the boundary of their home community. By extension, it can sometimes be any regular or often repeated travel between locations, even when not work-related. The modes of travel, time taken and distance traveled in commuting varies widely across the globe. Most people in least-developed countries continue to walk to work.
Effects of the car on societiesSince the start of the twentieth century, the role of cars has become highly important, though controversial. They are used throughout the world and have become the most popular mode of transport in many of the more developed countries. In developing countries, the effects of the car on society are not as visible, however they are nonetheless significant. The development of the car built upon the transport sector first started by railways. This has introduced sweeping changes in employment patterns, social interactions, infrastructure and the distribution of goods.
Set theorySet theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concerned with those that are relevant to mathematics as a whole. The modern study of set theory was initiated by the German mathematicians Richard Dedekind and Georg Cantor in the 1870s. In particular, Georg Cantor is commonly considered the founder of set theory.
Set (mathematics)A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets. The set with no element is the empty set; a set with a single element is a singleton. A set may have a finite number of elements or be an infinite set. Two sets are equal if they have precisely the same elements. Sets are ubiquitous in modern mathematics.
SuffixIn linguistics, a suffix is an affix which is placed after the stem of a word. Common examples are case endings, which indicate the grammatical case of nouns and adjectives, and verb endings, which form the conjugation of verbs. Suffixes can carry grammatical information (inflectional endings) or lexical information (derivational/lexical suffixes). Inflection changes the grammatical properties of a word within its . Derivational suffixes fall into two categories: class-changing derivation and class-maintaining derivation.
Natural capitalNatural capital is the world's stock of natural resources, which includes geology, soils, air, water and all living organisms. Some natural capital assets provide people with free goods and services, often called ecosystem services. All of these underpin our economy and society, and thus make human life possible. It is an extension of the economic notion of capital (resources which enable the production of more resources) to goods and services provided by the natural environment.
CarpoolCarpooling is the sharing of car journeys so that more than one person travels in a car, and prevents the need for others to have to drive to a location themselves. By having more people using one vehicle, carpooling reduces each person's travel costs such as: fuel costs, tolls, and the stress of driving. Carpooling is also a more environmentally friendly and sustainable way to travel as sharing journeys reduces air pollution, carbon emissions, traffic congestion on the roads, and the need for parking spaces.
