Recipe of Continuous Functions

  • Abraham Quansah
  • Nicholas Adjei-Boateng
  • Charlotte Anima Nketia KNUST

Abstract

A function 𝑅→𝑅 is continuous at a point π‘₯0,if for πœ€>0, there exist a 𝛿>0 such that |π‘₯βˆ’π‘₯π‘œ|<𝛿 implies


|𝑓(π‘₯)βˆ’π‘“( π‘₯π‘œ)|<πœ€. Therefore, the function f is a continuous function if it is continuous at every point. In the context of general topology, the β€˜small’ sets may be replaced by β€˜well-chosen open set’. So the definition should be thought of as: a function 𝑓 is continuous at π‘₯ if given any small enough open set U containing 𝑓(π‘₯), there is an open set V (that we may be forced to choose very small) containing π‘₯ such that 𝑓(𝑉)βŠ‚π‘ˆ. Continuity of a function depends not only upon the function 𝑓 itself, but also on the topologies specified for its domain and range.

Published
Sep 3, 2017
How to Cite
QUANSAH, Abraham; ADJEI-BOATENG, Nicholas; NKETIA, Charlotte Anima. Recipe of Continuous Functions. Journal of Mathematical Acumen and Research, [S.l.], v. 2, n. 2, sep. 2017. ISSN 2467-8929. Available at: <http://pubs.jomaar.org/index.php/jmr/article/view/26>. Date accessed: 17 oct. 2017.