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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.)
##### Keywords:
separating set; separated spaces
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