Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 19, No. 1, pp. 19-41 (2003)

Exploded and compressed spaces

I. Szalay

University of Szeged, Hungary

Abstract: Continuing the theory of exploded and compressed numbers the paper contains five parts. Part 1.: Introduction which contains the most important rules of computation with exploded and compressed numbers. Part 2.: This part contains the concept of explosion and compression of $k$-dimensional Euclidean space $R^k$ extending the concepts of traditional linear operations, inner product, norm and metric. We extend them for the case of several variables. Part 3.: Descriptions of lux phenomena which show the visible parts of objects in the exploded spaces. Part 4.: The beginning of analysis of functions with several variables defined on the exploded space. Part 5.: A few words on the geometry of the exploded three dimensional space with an interesting open problem for the traditional three dimensional space.

Keywords: Exploded numbers, exploded spaces, compressed spaces, super-lines, super-planes, super-spheres, window phenomenon, extra parallelness.

Classification (MSC2000): 03C30

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