# Continuous Functions

Keywords:
Review, Continuity, Topology

### Abstract

A polynomial function f is said to be continuous on an interval if it is continuous

at each and every point in the interval. Continuity at an endpoint, if one exists, means

f is continuous from the right ( for the left endpoint) or continuous from the left (for

the right endpoint). Usually, if we say a function is continuous, without specifying an

interval, we mean that it is continuous everywhere on the real line,i.e,the set of all real

numbers (−∞, ∞). Or that it is continuous at every point of its domain, if its domain does not include all real numbers.

### References

[1] Adams C, Franzosa R. Introduction to topology, pure and applied, Pearson Prentice Hall; 2008 .

[2] Obeng,W, Lecture notes on General Topology, KNUST-Ghana; 2017.

[3] Miller,K, Polynomials are continuous functions [online], September 22, 2014.Available from: http://math.berkeley.edu

[4] Rognes, J, Lecture notes on topology [online], November 29, 2010.Available from: http://www.folk.uio.no/rognes/kurs/ma

[5] Mathematics libreTexts: making online reading much easier. UC Davis Library, the California State University, April 27, 2019.Available from: http://www.mathematics.libretexts.org

[6] Paulsen, V, Lecture notes on Introduction to Real Analysis [online], November 6,2014.Available from: http://www.math.uh.edu

[7] Munkres, J.R, Topology, second edition, Prentice Hall inc. Englewood cliffs, N.J, 2000. MR. 57, No 2063.

[8] Continuity,[online],Available from: http://www.personal.psu.edu

[9] Continuous functions,[online],Available from: m:http//www3.nd.edu

[2] Obeng,W, Lecture notes on General Topology, KNUST-Ghana; 2017.

[3] Miller,K, Polynomials are continuous functions [online], September 22, 2014.Available from: http://math.berkeley.edu

[4] Rognes, J, Lecture notes on topology [online], November 29, 2010.Available from: http://www.folk.uio.no/rognes/kurs/ma

[5] Mathematics libreTexts: making online reading much easier. UC Davis Library, the California State University, April 27, 2019.Available from: http://www.mathematics.libretexts.org

[6] Paulsen, V, Lecture notes on Introduction to Real Analysis [online], November 6,2014.Available from: http://www.math.uh.edu

[7] Munkres, J.R, Topology, second edition, Prentice Hall inc. Englewood cliffs, N.J, 2000. MR. 57, No 2063.

[8] Continuity,[online],Available from: http://www.personal.psu.edu

[9] Continuous functions,[online],Available from: m:http//www3.nd.edu

Published

2019-12-30

Section

Articles