Topology Atlas Document # ppae-29


Quasiorders on topological categories

Vera Trnková

Proceedings of the Ninth Prague Topological Symposium (2001) pp. 321-330

We prove that, for every cardinal number a greater than or equal c, there exists a metrizable space X with |X|=a such that for every pair of quasiorders <= 1, <= 2 on a set Q with |Q| = a satisfying the implication
q <= 1 q' implies q <= 2 q'
there exists a system { X(q) : q in Q} of non-homeomorphic clopen subsets of X with the following properties:

Mathematics Subject Classification. 54B30 54H10.
Keywords. homeomorphism onto clopen subspace, onto closed subspace, quasiorder, metrizable spaces.

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Copyright © 2002 Charles University and Topology Atlas. Published April 2002.