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'point-free geometry'
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| Title of object: |
point-free geometry |
| Canonical Name: |
PointFreeGeometry |
| Type: |
Definition |
| Created on: |
2007-01-13 08:58:59 |
| Modified on: |
2007-01-13 15:25:36 |
| Classification: |
msc:03B10, msc:03B15 |
| Keywords: |
regions, Whitehead, mereology, mereotopology |
| Synonyms: |
point-free geometry=pointless geometry |
Revision comment (for changes between this and next version):
| Changes for correction #11242 ('typo'). |
Preamble:
% this is the default PlanetMath preamble. as your knowledge
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\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
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%\usepackage{psfrag}
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%\usepackage{graphicx}
% for neatly defining theorems and propositions
%\usepackage{amsthm}
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%\usepackage{xypic}
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Content:
Point-free geometry is based on the idea that in geometry it is not necessary to assume as a primitive the notion of point. Instead, we can start from the notion of a region in the space and the points are defined by suitable \textit{abstraction processes}, i.e. order-reversing sequences of regions. Firstly, such a question was analized by A. N. Whitehead in the books "An Inquiry Concerning the Principles of Natural Knowledge" and "The concept of Nature" in which the inclusion relation is a primitive. Successively in "Process and Reality" Whitehead proposed a new approach in which the connection relation is considered.
\textbf{References}
1. A. N. Whitehead, An Inquiry Concerning the Principles of Natural Knowledge, Cambr. Univ. Press, Cambrige 1919.
2. A. N. Whitehead, The concept of Nature, Cambr. Univ. Press, Cambrige 1920.
3. A. N. Whitehead, Process and Reality, The Macmillan Co., New York 1929.
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