On the geometric concomitants

Zenon Moszner

Abstract


In this note the necessary and sufficient conditon it would the concomitant of the geometric object was the geometric object too is given.

Keywords


object; geometric object; concomitant; translation equation; concomitant equation

Mathematics Subject Classification (2010)


39B52; 51M05

References


Aczél, J. and S. Gołab. Funktionalgleichungen der Theorie der geometrischen Objekte. Vol. 39 of Mathematical Monographs. Warsaw: PWN - Polish Scientific Publishers, 1960.

Baron, K., W. Chojnacki and W. Jarczyk. "Continuity of solutions of the translation equation." Aequationes Math. 74, no. 3 (2007): 314-317.

Bourbaki, N. Éléments de mathématique. Part I. Les structures fondamentales de l’analyse. Livre II. Algèbre. Chapitre I. Structures algébriques. Vol. 934 of Actual. Sci. Ind. Paris: Hermann et Cie., 1942.

Gołab, S. "Sur quelques points concernant la notion du comitant." Annales Soc. Pol. Math. 17 (1938): 17-192.

Kucharzewski, M. and M. Kuczma. Basic concepts of the theory of geometric objects. Vol. 43 of Dissertationes Mathematicae. Warsaw: Instytut Matematyczny Polskiej Akademii Nauk, 1964

Moszner, Z. "Sur l’équation du comitant." Tensor (N.S.) 51, no. 3 (1992): 205-208.

Moszner, Z. "Miscellanea about the stability of functional equations." In Ulam’s Type Stability, 213-250. Cham: Springer International Publishing AG, 2019.

Sibirsky, K.S. Introduction to topological dynamics. Leide: Noordhoff International Publishing, 1975.

Starke, P.H. Abstract automata. Amsterdam-London: North-Holland Publishing Co.; New York: American Elsevier Publishing Co., Inc., 1972.


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