Local Functions and Composition With Euclidean Smooth Functions
Abstract
In [2] the local function on a nonempty set and the composition with Euclidean smooth functions are defined for collection of functions , which is an abstract generalization of the collection of functions on the Euclidean space [12]. This paper provides local functions and composition with Euclidean smooth functions for a countable set of functions . Important theorems and examples concerning local functions and composition with Euclidean smooth functions are given.
Keywords:
Functions concept
initial topology
partial derivatives
smooth functions
How to Cite
Ebtesam Abdullah Alousta. (2023). Local Functions and Composition With Euclidean Smooth Functions. Bani Waleed University Journal of Humanities and Applied Sciences, 8(5), 530-540. https://doi.org/10.58916/jhas.v8i5.107
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References
1.
1 R. Brown, Elements of Modern Topology (Mcgraw-Hill Book Company, New York 1968).
2.
2 T. Bulati, Y. EL-Edresi, E. Ousta, “ Initial differential spaces,” Proccedings of the First Conference of Mathematical Sciences, Zerqa Private University, Jordan, (2006), 217-222.
3.
3 J. Gruszczak, M. Heller, P. Multarzynski, “ A generalization of manifolds as space-time models,” J. Math. Phys., 29 (1988), 2576-2580.
4.
M. Heller, P. Multarzynski, W. Sasin, Z. Zekanowski, “ On some generalizations of the manifold concept,” Acta Cosmologica-Fasciculus, 18 (1992), 31-44.
5.
M. Heller, W. Sasin, “ The structure of the b-completion of space-time,” General Relativity and Gravitation, 26 (1994), 797-811.
6.
M. Heller, W. Sasin, “ Structured spaces and their application to relativistic physics,” J. Math. Phys. , 36 (7) (1995).
7.
I. N. Herstein, Topics in Algebra ((2nd ed. ). Lexington, Mass. : Xerox College Publishing, 1975).
8.
P. Multarzynski, W. Sasin, “ Algebraic characterization of the dimension of differential spaces,” Rened. Circ. Mat. Parbrmo (2) Suppl. (1990), 193-199.
9.
B. O’Neill, Elementary Differential Geometry (New York, N. Y. : A Cademic Press, 1966).
10.
W. Sasin, Z. Zekanowski, “ On some sheaves over a differential space,” Arch. Math. 4, Scripta Fac. Sci. Nat. Ujep Brunensis, 18 (1982), 193-199.
11.
W. Sasin, “ Differential spaces and singularities in differential space-times,” Demonstratio Math., 24(1991), 601-634.
12.
R. Sikorski, “ Differential modules,” Colloquium Mathematical, 24 (1971), 45-79.
13.
W. Waliszewski, “ On a coregular division of a differential space by an equivalence relation,” Colloquium Mathematicum, 26(1972), 281-291.
14.
W. Waliszewski, “ Regular and coregular mappings of differential spaces,” Ann. Polon. Math., 30 (1975), 263-281.
