This article is cited in 6 papers

Geometry and topology

On attractors of iterated function systems in uniform spaces

M. Samuel^a, A. V. Tetenov<sup>bc

a</sup> Department of Mathematics, Bharatha Mata College, Kochi, India
^b Novosibirsk State University
^c Gorno-Altaisk State University

Abstract: We prove Hutchinson's theorem for uniform spaces, that a finite system $\mathcal{S}$ of $\mathcal{B}$-contractions in complete, well-chained, Hausdorff uniform space defines unique compact attractor.

Keywords: self-similar set, uniform space, $\mathcal{B}$-contraction, asymptotical regularity.

UDC: 514.8, 515.12

MSC: 28A80

Received December 10, 2016, published March 1, 2017

Language: English

DOI: 10.17377/semi.2017.14.015

Bibliographic databases:

•