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Representation of standard Liebchtz functions under a microscope | ||
| Journal of Education and Science | ||
| Article 27, Volume 25, Issue 1, 2012, Pages 120-127 PDF (0 K) | ||
| DOI: 10.33899/edusj.2012.58986 | ||
| Authors | ||
| Taher Ismail; Hind Saleh | ||
| Abstract | ||
| ABSTRACT The aim of this paper is to provide a representation of a standard lipschitzian functions by mean of a microscope. More precisely, under certain conditions, the following results have been obtained. Let be a standard function, and be the shadow of its graph : (i) If is s-continuous and limited, then is the graph of a continuous function on . (ii) If is continuous and if is the graph of a function defined on , then is a continuous function. The standard function is lipschitzian at a neighbourhood of a standard point if and only if is limited under every microscope of power centered at a point or at a point infinitely close to it. If the standard function is lipschitzian at a neighbourhood of a standard point ,then it's representation under a microscopic of power centered at the point or at a point infinitely close to it, is a graph of a lipschitzian function. | ||
| Keywords | ||
| standard Liebchtz; functions; microscope | ||
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