The narrow border between a continuous function and a discontinuous function
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Author(s)
Abstract
The RAFU functions have been studied in [1, 2, 3, 4, 5 and 6]. They are useful in Approximation Theory to approach continuous functions and to reconstruct continuous functions. In this work we will use the RAFU functions to turn a discontinuous function into a continuous function. We will show the explicit expression of a sequence of continuous functions that converges to a discontinuous function given except at its discontinuity points. The paper shows examples for different types of discontinuities.
Keywords
RAFU functions; continuous functions; discontinuous functions.
Cite this paper
Alicia C. Sánchez,
The narrow border between a continuous function and a discontinuous function
, SCIREA Journal of Mathematics.
Volume 5, Issue 3, June 2020 | PP. 32-43.
References
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[ 6 ] | E Corbacho. Uniform reconstruction of continuous functions with the RAFU method. Applied General Topology 18 (2). 361-375. 2017. |