Properties of continuous functions on a compact

Authors

  • Dheaa Kamel Hussain Al-Janabi Mustansiriya University Iraq - Bogdad, Almustansiriya, 46007, Iraq

DOI:

https://doi.org/10.15587/1729-4061.2013.16341

Keywords:

continuous functions, compactness, The Weierstrass theorem, The Cauchy theorem

Abstract

The work deals with the definition of a continuous function, definitions of a continuous function by Cauchy, Heine, in the increment language.

The properties of continuous functions on a compact (on an interval) have been studied comprehensively. The 1st and the 2nd Weierstrass theorems, the 1st and the 2nd Cauchy theorems are presented, as well as the main corollaries of them.

The proofs of theorems and corollaries are presented step by step. Sequentially compact sets are important because continuous functions defined on sequentially compact sets have some very useful properties, which they do not have in general when defined on non-compact sets

Author Biography

Dheaa Kamel Hussain Al-Janabi, Mustansiriya University Iraq - Bogdad, Almustansiriya, 46007

CollegeofEducation

The Department of mathematics

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Published

2013-08-14

How to Cite

Al-Janabi, D. K. H. (2013). Properties of continuous functions on a compact. Eastern-European Journal of Enterprise Technologies, 4(4(64), 55–57. https://doi.org/10.15587/1729-4061.2013.16341

Issue

Vol. 4 No. 4(64) (2013): Mathematics and cybernetics - applied aspects

Section

Mathematics and Cybernetics - applied aspects

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Copyright (c) 2014 Dheaa Kamel Hussain Al-Janabi

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