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Transfinite extension of Steinke’s dimension. (English) Zbl 0963.54024
Summary: We introduce a transfinite extension trt of dimension \(t\) from G. Steinke [Arch. Math. 40, 273-282 (1983; Zbl 0492.54021)]. We extend all main theorems for \(t\) such as the sum theorems, the product theorem and the compactification theorem to the transfinite numbers. We also consider the class of all spaces \(X\) with trt\( (X)=\omega_0\), the so-called finite-dimensional separated spaces [F. G. Arenas and M. L. Puertas, Publ. Math. 54, No. 1-2, 21-31 (1999; Zbl 0924.54040)], with respect to the usual classes of infinite-dimensional spaces.

MSC:
54F45 Dimension theory in general topology
54B10 Product spaces in general topology
54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.)
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