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On Mapping Sequences of a Projective Spectrum

In: A Lost Mathematician, Takeo Nakasawa

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  • Takeo Nakasawa

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.

Suggested Citation

  • Takeo Nakasawa, 2009. "On Mapping Sequences of a Projective Spectrum," Springer Books, in: Hirokazu Nishimura & Susumu Kuroda (ed.), A Lost Mathematician, Takeo Nakasawa, pages 223-234, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7643-8573-6_14
    DOI: 10.1007/978-3-7643-8573-6_14
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