Compact metric spaces as minimal-limit sets in domains of bottomed sequences

• DOI: 10.1017/s0960129504004396
• Publication Date: 2004-11-16T10:28:09Z
• Authors: HIDEKI TSUIKI
• Keywords: Retract; Direct limit; Limit set

Every compact metric space $X$ is homeomorphically embedded in an $\omega$-algebraic domain $D$ as the set of minimal limit (that is, non-finite) elements. Moreover, a retract $L(D)$ all elements $D$. Such can be chosen so that it has property M and finite-branching, height equal to small inductive dimension $X$. We also show topological for domains with M. These results give characterisation which The we embed $n$-dimensional ($n \leq \infinity$) concrete structure consists finite/infinite sequences $\{0,1,\bot\}$ at most $n$ copies $\bot$.