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A Lost Mathematician, Takeo NakasawaOn Mapping Sequences of a Projective Spectrum

A Lost Mathematician, Takeo Nakasawa: On Mapping Sequences of a Projective Spectrum [In the present work we will introduce two new notions, i.e., mapping sequence and projective point sequence, and by these notions, we study what one may call Alexandroff’s Homeomorphism Theorem1. Namely by means of mapping sequences, we will divide that theorem into several homeomorphism theorems which clearly express the topological character of the mapping sequences, and by the use of projective point sequences, we simplify the proofs of these theorems. Then, we will give a proof of Borsuk’s2 theorem by making use of the notion of mapping sequences. Finally, we consider an extension of the notion of a mapping sequence, and a few results are derived from this extension. ] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A Lost Mathematician, Takeo NakasawaOn Mapping Sequences of a Projective Spectrum

Editors: Nishimura, Hirokazu; Kuroda, Susumu
Nakasawa, Takeo
A Lost Mathematician, Takeo Nakasawa — Dec 13, 1937
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Publisher
Birkhäuser Basel
Copyright
© Birkhäuser Basel 2009
ISBN
978-3-7643-8572-9
Pages
223 –234
DOI
10.1007/978-3-7643-8573-6_14
Publisher site
See Chapter on Publisher Site

Abstract

[In the present work we will introduce two new notions, i.e., mapping sequence and projective point sequence, and by these notions, we study what one may call Alexandroff’s Homeomorphism Theorem1. Namely by means of mapping sequences, we will divide that theorem into several homeomorphism theorems which clearly express the topological character of the mapping sequences, and by the use of projective point sequences, we simplify the proofs of these theorems. Then, we will give a proof of Borsuk’s2 theorem by making use of the notion of mapping sequences. Finally, we consider an extension of the notion of a mapping sequence, and a few results are derived from this extension. ]

Published: Dec 13, 1937

Keywords: Continuous Mapping; Mapping Space; Simplicial Mapping; Wide Sense; Mapping Sequence

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