Ott, Tomforde and Willis proposed a useful compactification for one-sided shifts over infinite alphabets. Building from their idea, we develop a notion of two-sided shift spaces over infinite alphabets, with an eye towards generalizing a result of Kitchens. As with the one-sided shifts over infinite alphabets, our shift spaces are compact Hausdor spaces but, in contrast to the one-sided setting, our shift map is continuous everywhere.We show that many of the classical results from symbolic dynamics are still true for our twosided shift spaces. In particular, while for one-sided shifts the problem about whether or not any M-step shift is conjugate to an edge shift space is open, for two-sided shifts we can give a positive answer for this question.

Additional Metadata
Keywords Infinite alphabet shift spaces, Symbolic dynamics, Two-sided shift spaces
Persistent URL dx.doi.org/10.1017/S1446788717000039
Journal Journal of the Australian Mathematical Society
Citation
Gonçalves, D. (Daniel), Sobottka, M. (Marcelo), & Starling, C. (2017). Two-sided shift spaces over infinite alphabets. Journal of the Australian Mathematical Society, 103(3), 357–386. doi:10.1017/S1446788717000039