Local Functions and Composition With Euclidean Smooth Functions
DOI:
https://doi.org/10.58916/jhas.v8i5.107الكلمات المفتاحية:
مفهوم الدوال، الطوبولوجيا الأولية، المشتقات الجزئية، الدوال الملساءالملخص
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.
التنزيلات
المراجع
1 R. Brown, Elements of Modern Topology (Mcgraw-Hill Book Company, New York 1968).
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 J. Gruszczak, M. Heller, P. Multarzynski, “ A generalization of manifolds as space-time models,” J. Math. Phys., 29 (1988), 2576-2580.
M. Heller, P. Multarzynski, W. Sasin, Z. Zekanowski, “ On some generalizations of the manifold concept,” Acta Cosmologica-Fasciculus, 18 (1992), 31-44.
M. Heller, W. Sasin, “ The structure of the b-completion of space-time,” General Relativity and Gravitation, 26 (1994), 797-811.
M. Heller, W. Sasin, “ Structured spaces and their application to relativistic physics,” J. Math. Phys. , 36 (7) (1995).
I. N. Herstein, Topics in Algebra ((2nd ed. ). Lexington, Mass. : Xerox College Publishing, 1975).
P. Multarzynski, W. Sasin, “ Algebraic characterization of the dimension of differential spaces,” Rened. Circ. Mat. Parbrmo (2) Suppl. (1990), 193-199.
B. O’Neill, Elementary Differential Geometry (New York, N. Y. : A Cademic Press, 1966).
W. Sasin, Z. Zekanowski, “ On some sheaves over a differential space,” Arch. Math. 4, Scripta Fac. Sci. Nat. Ujep Brunensis, 18 (1982), 193-199.
W. Sasin, “ Differential spaces and singularities in differential space-times,” Demonstratio Math., 24(1991), 601-634.
R. Sikorski, “ Differential modules,” Colloquium Mathematical, 24 (1971), 45-79.
W. Waliszewski, “ On a coregular division of a differential space by an equivalence relation,” Colloquium Mathematicum, 26(1972), 281-291.
W. Waliszewski, “ Regular and coregular mappings of differential spaces,” Ann. Polon. Math., 30 (1975), 263-281.
التنزيلات
منشور
إصدار
القسم
كيفية الاقتباس
