Topology Proceedings
Document # baak-20
Electronic Version 24 Summer (1999) |
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The approximation of continua by T1/2-spaces
R. D. Kopperman, I. Puga and R. G. Wilson
A special case of a classical result of Alexandroff states that every one dimensional metric continuum is the inverse limit of a sequence of one dimensional polyhedra, otherwise known as finite graphs. Since a compact Hausdorff space is the Hausdorff reflection of an inverse limit of finite T0-spaces, it is natural to ask whether one dimensional metric continua are the inverse limits of connected T0-spaces which are one dimensional in some sense. This paper shows that each one dimensional metric continuum can be characterized as the Hausdorff reflection of the limit of an inverse sequence with special bonding maps of connected finite T0-spaces whose order or Alexandroff dimension (defined below) is one.
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Date published electronically: March 5, 2001.