In mathematics, the support of a function is the set of points where the function is not zero-valued or, in the case of functions defined on a topological space, the closure of that set. This concept is used very widely in mathematical analysis. In the form of functions with support that is bounded, it also plays a major part in various types of mathematical duality theories.
Suppose that f: X→R is a real-valued function whose domain is an arbitrary set X. The set-theoretic support of f, written supp(f), is the set of points in X where f is non-zero
The support of f is the smallest subset of X with the property that f is zero on the subset's complement, meaning that the non-zero values of f "live" on supp(f). If f(x)=0 for all but a finite number of points xinX, then f is said to have finite support.
If the set X has an additional structure (for example, a topology), then the support of f is defined in an analogous way as the smallest subset of X of an appropriate type such that f vanishes in an appropriate sense on its complement. The notion of support also extends in a natural way to functions taking values in more general sets than R and to other objects, such as measures or distributions.
Service provision is often an economic activity where the buyer does not generally, except by exclusive contract, obtain exclusive ownership of the thing purchased. The benefits of such a service, if priced, are held to be self-evident in the buyer's willingness to pay for it. Public services are those, that society (nation state, fiscal union, regional) as a whole pays for, through taxes and other means.
By composing and orchestrating the appropriate level of resources, skill, ingenuity, and experience for effecting specific benefits for service consumers, service providers participate in an economy without the restrictions of carrying inventory (stock) or the need to concern themselves with bulky raw materials. On the other hand, their investment in expertise does require consistent service marketing and upgrading in the face of competition.
Business services are a recognisable subset of Economic services, and share their characteristics. The essential difference is that Business are concerned about the building of Service Systems in order to deliver value to their customers and to act in the roles of Service Provider and Service Consumer.
The generic clear-cut, complete, concise and consistent definition of the service term reads as follows:
A service is a set of one time consumable and perishable benefits
delivered from the accountable service provider, mostly in close coaction with his internal and external service suppliers,
effectuated by distinct functions of technical systems and by distinct activities of individuals, respectively,
commissioned according to the needs of his service consumers by the service customer from the accountable service provider,
rendered individually to an authorized service consumer at his/her dedicated trigger,
and, finally, consumed and utilized by the triggering service consumer for executing his/her upcoming business activity or private activity.
Offshore (1979) is a novel by Penelope Fitzgerald. It won the Booker Prize for that year. It recalls her time spent on boats on the Thames in Battersea. The novel explores the liminality of people who do not belong to the land or the sea, but are somewhere in between. The epigraph, "che mena il vento, e che batte la pioggia, e che s'incontran con si aspre lingue" ("whom the wind drives, or whom the rain beats, or those who clash with such bitter tongues") comes from Canto XI of Dante's Inferno.