We say that a topological space X is Volterra if for each pair f, g: X→ℝ for which the sets of points at which f, respectively g, are continuous are dense, there is a common point of continuity; and X is strongly Volterra if in the same circumstances the set of common points of continuity is dense in X. For both of these concepts equivalent conditions are given and the situation involving more than two functions is explored.

In this paper we examine the properties of EC-plastic metric spaces, spaces which have the property that any noncontractive bijection from the space onto itself must be an isometry.  2005 Elsevier Inc. All rights reserved.

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The paper presents an overview of current and expected prospects for the development of artificial intelligence algorithms, especially in military applications, and conducted research regarding applications in the area of civilian life. Attention was paid mainly to the use of AI algorithms in cybersecurity, object detection, military logistics and robotics. It discusses the problems connected with the present solutions and how artificial intelligence can help solve them. It briefly presents also mathematical structures and descriptions for ART, CNN and SVM networks as well as Expectation–Maximization and Gaussian Mixture Model algorithms that are used in solving of discussed problems. The third chapter discusses the attitude of society towards the use of neural network algorithms in military applications. The basic problems related to ethics in the application of artificial intelligence and issues of responsibility for errors made by autonomous systems are discussed.

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