Varieties of continua : from regions to points and back / Geoffrey Hellman and Stewart Shapiro.

Varieties of continua : from regions to points and back / Geoffrey Hellman and Stewart Shapiro.

First edition.

9780191781087 (electronic book)

Oxford : Oxford University Press, 2018.

English

1 online resource : illustrations

B105.C5

515.222

Two historical episodes form the background to the research presented here: the first is the remarkably rapid transition in the course of the nineteenth century from the ancient Aristotelian view that a true continuum cannot be composed entirely of points to the now standard, entirely punctiform frameworks for analysis and geometry found in modern texts. The second is the mid-to-late 20th-century revival of pre-limit methods in analysis and geometry using infinitesimals, viz. non-standard analysis due to Abraham Robinson, and the more radical smooth infinitesimal analysis based on intuitionistic logic. One goal of this work is to develop a systematic comparison of these. A second goal is to develop thoroughgoing regions-based theories of classical continua that are mathematically equivalent to the currently standard, punctiform accounts of modern texts.

Two historical episodes form the background to the research presented here: the first is the remarkably rapid transition in the course of the nineteenth century from the ancient Aristotelian view that a true continuum cannot be composed entirely of points to the now standard, entirely punctiform frameworks for analysis and geometry found in modern texts. The second is the mid-to-late 20th-century revival of pre-limit methods in analysis and geometry using infinitesimals, viz. non-standard analysis due to Abraham Robinson, and the more radical smooth infinitesimal analysis based on intuitionistic logic. One goal of this work is to develop a systematic comparison of these. A second goal is to develop thoroughgoing regions-based theories of classical continua that are mathematically equivalent to the currently standard, punctiform accounts of modern texts.

Includes bibliographical references and index.

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Description based on online resource; title from home page (viewed on February 20, 2018).

Print version: 9780198712749

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