Some Properties of Real Maps

Adam Grabowski

University of Bialystok

This paper was written while the author visited the Shinshu University in the winter of 1997.

Yatsuka Nakamura

Shinshu University, Nagano

Summary.

The main goal of the paper is to show logical equivalence of the two definitions of the {\em open subset}: one from [3] and the other from [21]. This has been used to show that the other two definitions are equivalent: the continuity of the map as in [19] and in [20]. We used this to show that continuous and one-to-one maps are monotone (see theorems 16 and 17 for details).

MML Identifier: JORDAN5A

Contents (PDF format)

1. Preliminaries
2. Equivalence of analytical and topological definitions of continuity
3. On the monotonicity of continuous maps

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