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General Algebra of Analysis

In: Selecta Mathematica

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  • Karl Menger

Abstract

The classical presentation of projective geometry starts with a class of undefined entities, called points. Lines are introduced as undefined sets of points satisfying some basic postulates. Planes are defined as sets of points with certain properties. With the transition to each higher dimension new concepts must be introduced. The fundamental operations of projective geometry, that is, joining and intersecting, are set-theoretically defined. The algebraic properties of these operations are immediate consequences of these definitions on which the classical theory does not elaborate.

Suggested Citation

  • Karl Menger, 2003. "General Algebra of Analysis," Springer Books, in: Bert Schweizer & Abe Sklar & Karl Sigmund & Peter Gruber & Edmund Hlawka & Ludwig Reich & Leopold Sc (ed.), Selecta Mathematica, pages 189-203, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7091-6045-9_21
    DOI: 10.1007/978-3-7091-6045-9_21
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