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James Embedding
In mathematics, the James embedding is an embedding of a real, complex, or hyperbolic projective space into a sphere, introduced by Ioan James Ioan Mackenzie James FRS (born 23 May 1928) is a British mathematician working in the field of topology, particularly in homotopy theory. Biography James was born in Croydon, Surrey, England, and was educated at St Paul's School, London and .... References Algebraic topology {{topology-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Projective Space
In mathematics, the concept of a projective space originated from the visual effect of perspective, where parallel lines seem to meet ''at infinity''. A projective space may thus be viewed as the extension of a Euclidean space, or, more generally, an affine space with points at infinity, in such a way that there is one point at infinity of each direction of parallel lines. This definition of a projective space has the disadvantage of not being isotropic, having two different sorts of points, which must be considered separately in proofs. Therefore, other definitions are generally preferred. There are two classes of definitions. In synthetic geometry, ''point'' and ''line'' are primitive entities that are related by the incidence relation "a point is on a line" or "a line passes through a point", which is subject to the axioms of projective geometry. For some such set of axioms, the projective spaces that are defined have been shown to be equivalent to those resulting from the fol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ioan James
Ioan Mackenzie James FRS (born 23 May 1928) is a British mathematician working in the field of topology, particularly in homotopy theory. Biography James was born in Croydon, Surrey, England, and was educated at St Paul's School, London and Queen's College, Oxford. In 1953 he earned a D. Phil. from the University of Oxford for his thesis entitled ''Some problems in algebraic topology'', written under the direction of J. H. C. Whitehead. In 1957 he was appointed reader in pure mathematics, a post which he held until 1969. From 1959 until 1969 he was a senior research fellow at St John's College. He held the Savilian Chair of Geometry at the University of Oxford from 1970 to 1995. He is now a professor emeritus. He was elected a Fellow of the Royal Society in 1968. In 1978 the London Mathematical Society awarded him the Senior Whitehead Prize, which was established in honour of his doctoral supervisor, Whitehead. In 1984 he became President of the London Mathematical Society ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
