Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990 Association of Mizar Users

Real Function Uniform Continuity


Jaroslaw Kotowicz
Warsaw University, Bialystok
Konrad Raczkowski
Warsaw University, Bialystok

Summary.

The uniform continuity for real functions is introduced. More theorems concerning continuous functions are given. (See [10]) The Darboux Theorem is exposed. Algebraic features for uniformly continuous functions are presented. Various facts, e.g., a continuous function on a compact set is uniformly continuous are proved.

Supported by RPBP.III-24.C8.

MML Identifier: FCONT_2

The terminology and notation used in this paper have been introduced in the following articles [12] [14] [1] [13] [3] [2] [9] [15] [5] [4] [6] [7] [8] [11] [10]

Contents (PDF format)

Bibliography

[1] Grzegorz Bancerek. The ordinal numbers. Journal of Formalized Mathematics, 1, 1989.
[2] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[3] Krzysztof Hryniewiecki. Basic properties of real numbers. Journal of Formalized Mathematics, 1, 1989.
[4] Jaroslaw Kotowicz. Convergent real sequences. Upper and lower bound of sets of real numbers. Journal of Formalized Mathematics, 1, 1989.
[5] Jaroslaw Kotowicz. Real sequences and basic operations on them. Journal of Formalized Mathematics, 1, 1989.
[6] Jaroslaw Kotowicz. Partial functions from a domain to a domain. Journal of Formalized Mathematics, 2, 1990.
[7] Jaroslaw Kotowicz. Partial functions from a domain to the set of real numbers. Journal of Formalized Mathematics, 2, 1990.
[8] Jaroslaw Kotowicz. Properties of real functions. Journal of Formalized Mathematics, 2, 1990.
[9] Jan Popiolek. Some properties of functions modul and signum. Journal of Formalized Mathematics, 1, 1989.
[10] Konrad Raczkowski and Pawel Sadowski. Real function continuity. Journal of Formalized Mathematics, 2, 1990.
[11] Konrad Raczkowski and Pawel Sadowski. Topological properties of subsets in real numbers. Journal of Formalized Mathematics, 2, 1990.
[12] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[13] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
[14] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[15] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.

Received June 18, 1990

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