Intermediate Value Theorem and Thickness of Simple Closed Curves

Yatsuka Nakamura

Shinshu University, Nagano

Andrzej Trybulec

University of Bialystok

Summary.

Various types of the intermediate value theorem ( [14]) are proved. For their special cases, the Bolzano theorem is also proved. Using such a theorem, it is shown that if a curve is a simple closed curve, then it is not horizontally degenerated, neither is it vertically degenerated.

MML Identifier: TOPREAL5

Contents (PDF format)

1. Intermediate Value Theorems and Bolzano Theorem
2. Simple Closed Curves Are Not Flat

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