Extensional Dimension and Completion of Maps
نویسنده
چکیده
We prove the following completion theorem for closed maps between metrizable spaces: Let f : X → Y be a closed surjection between metrizable spaces with e-dimf ≤ K, e-dimX ≤ LX and e-dimY ≤ LY for some countable CW -complexes K, LX and LY . Then there exist completions X̃ and Ỹ of X and Y , respectively, and a closed surjection f̃ : X̃ → Ỹ extending f such that e-dimf̃ ≤ K, e-dimX̃ ≤ LX and e-dimỸ ≤ LY . We also establish a parametric version of a result of Katetov characterizing the covering dimension of metrizable spaces in terms of uniformly 0-dimensional maps into finite-dimensional cubes.
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تاریخ انتشار 2003