This article is cited in 3 papers

Large Systems

Superpositions of continuous functions defined on a Baire space

S. S. Marchenkov, S. I. Krivospitsky

M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Abstract: We consider uniformly continuous functions on a Baire space and introduce the notion of a continuity modulus of a function. We formulate a condition on the growth of the continuity modulus $\varphi$ guaranteeing that superpositions of $n$-ary functions with continuity modulus $\varphi$ do not exhaust all $(n+1)$-ary functions with continuity modulus $\varphi$ for any $n$. Moreover, negating this property leads to the inverse effect.

UDC: 621.391.1+519.2

Received: 17.06.2009
Revised: 10.09.2009

 English version: Problems of Information Transmission, 2009, 45:4, 393–399

Bibliographic databases:

• 
• 
• 
• 
•