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I. M. JAMES In this article I have tried to describe, fairly briefly, what is known about the minimum dimension of euclidean space in which projective spaces, of various dimensions, can be (i) embedded, (ii) immersed. The bibliography, which I hope is tolerably complete, gives an idea of the amount of interest there has been in problems of this kind over the past 30 years or so. For reasons of space it is impossible to give a step-by-step account of the progress of the subject. Instead I have attempted, in the first half of this article, to put down a few words about each of the lines of approach which it seems essential to mention, and in the second half to summarize the present position, so far as specific results are concerned. References to the literature are given to assist the reader in search of further details, and do not necessarily include everything on a particular subject. I am most grateful to Professor S. Gitler, Professor K. Y. Lam, Dr. E. Rees and Dr. B. F . Steer for having read this article at the preprint stage; their comments have led to a number of improvements. The table at
Bulletin of the London Mathematical Society – Wiley
Published: Nov 1, 1971
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