O principal objetivo deste trabalho é o estudo de certas álgebras de funções complexas infinitamente deriváveis. Denomidas Álgebras de Dales-Davie, apresentamos a construção dessas álgebras que foram definidas por Dales e Davie em 1973, como também apresentamos os principais resultados envolvendo sua completude e naturalidade, tópicos que foram estudados por diversos autores, e.g. Abtahi, Honary, et al. Por fim, apresentamos os resultados obtidos por Lourenço e Vieira a respeito do estudo da diferença das álgebras de Dales-Davie com a Álgebra de Disco. / The main purpose of this work is to study the Dales-Davie algebras . We shall present the construction of this algebras defined by Dales and Davie in 1973. Following, the main results about its completeness and naturality as an normed algebra, this topics were studied by some authors, e.g. Abtahi, Honary, et al. Furthermore, we study the results found by Lourenço e Vieira about the difference of Dales-Davie algebras and Disk algebra.

A cathedral of the Church of England is the seat of the bishop and a centre of worship and mission. The history of this institution is followed from the English Reformation, which it survived, through to the Commonwealth, which it did not. Restored on the return of the monarchy, it then survived with little further trouble until the nineteenth century, when a lot of its income was diverted to the provision of churches and ministers for the populous urban and industrialised areas, which the Church could not fund in any other way. It was the subject of investigation by two Royal Commissions in the nineteenth century and three church-inspired commissions in the twentieth. These commissions stressed the links that should exist between cathedral, bishop and diocese, which the nineteenth century diocesan revival also encouraged, and suggested changes in instruments of governance to achieve this. Some proposals came to nothing, but others were brought into law. Unlike the Roman Catholic cathedral, the Anglican one never lost its autonomy. The religious situation in Britain today is considered in the light of some contemporary sociology and psychology, and it is recognised that the continued decline in the fortunes of the Church is tied up with the massive subjective turn which characterises contemporary culture. The cathedral has not shared the mistrust which faces the Church, and its various roles are discussed in the light of its continued hold on public affection. The conclusions reached are that, although the cathedral now has strong links with bishop and diocese, it should retain its independence within relationships of interdependence with them, to enable it to harness the popularity which it enjoys to remain a centre of worship, but primarily to concentrate on being a centre of mission. Appropriate ways of achieving that are discussed.