Topology Proceedings
Document # baam-81
Topology Proceedings 29 No. 1 (2005), pp. 377-384 |
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Extensional dimension and completion of maps
H. Murat Tuncali, E. D. Tymchatyn and Vesko Valov
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-dim f £ K,
e-dim X £ LX, and e-dim Y £ LY
for some countable CW-complexes K, LX, and LY. Then there exist
completions [X\tilde] and [Y\tilde] of X and Y,
respectively, and a closed surjection [f\tilde] : [X\tilde] ® [Y\tilde] extending f such that
e-dim[f\tilde] £ K,
e-dim[X\tilde] £ LX, and e-dim[Y\tilde] £ LY. We also establish a parametric version of a
result of Miroslav Katetov characterizing the covering dimension of
metrizable spaces in terms of uniformly 0-dimensional maps into
finite-dimensional cubes.
Keywords: finite-dimensional spaces, regularly branched maps
Mathematics Subject Classification: 54F45 (55M10 54C65)
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Topology Proceedings,
Volume 29, No. 1 (2005)
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