Monotonic and Continuous Real Function

Jaroslaw Kotowicz

Warsaw University, Bialystok

Summary.

A continuation of [13] and [11]. We prove a few theorems about real functions monotonic and continuous on interval, on halfline and on the set of real numbers and continuity of the inverse function. At the beginning of the paper we show some facts about topological properties of the set of real numbers, halflines and intervals which rather belong to [14].

MML Identifier: FCONT_3

Contents (PDF format)

Bibliography

[1] Grzegorz Bancerek. The fundamental properties of natural numbers. Journal of Formalized Mathematics, 1, 1989.

[2] Grzegorz Bancerek. The ordinal numbers. Journal of Formalized Mathematics, 1, 1989.

[3] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.

[4] Czeslaw Bylinski. Partial functions. Journal of Formalized Mathematics, 1, 1989.

[5] Krzysztof Hryniewiecki. Basic properties of real numbers. Journal of Formalized Mathematics, 1, 1989.

[6] Jaroslaw Kotowicz. Convergent sequences and the limit of sequences. Journal of Formalized Mathematics, 1, 1989.

[7] Jaroslaw Kotowicz. Real sequences and basic operations on them. Journal of Formalized Mathematics, 1, 1989.

[8] Jaroslaw Kotowicz. The limit of a real function at infinity. Journal of Formalized Mathematics, 2, 1990.

[9] Jaroslaw Kotowicz. Partial functions from a domain to a domain. Journal of Formalized Mathematics, 2, 1990.

[10] Jaroslaw Kotowicz. Properties of real functions. Journal of Formalized Mathematics, 2, 1990.

[11] Jaroslaw Kotowicz and Konrad Raczkowski. Real function uniform continuity. Journal of Formalized Mathematics, 2, 1990.

[12] Jan Popiolek. Some properties of functions modul and signum. Journal of Formalized Mathematics, 1, 1989.

[13] Konrad Raczkowski and Pawel Sadowski. Real function continuity. Journal of Formalized Mathematics, 2, 1990.

[14] Konrad Raczkowski and Pawel Sadowski. Topological properties of subsets in real numbers. Journal of Formalized Mathematics, 2, 1990.

[15] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.

[16] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.

[17] Andrzej Trybulec and Czeslaw Bylinski. Some properties of real numbers operations: min, max, square, and square root. Journal of Formalized Mathematics, 1, 1989.

[18] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.

[19] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.