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Abstract
The concept of relative topological finiteness is introduced. A Hausdorff compact space is constructed, which is homeomorphic to none of its proper Gδ-subspaces, but is homeomorphic to its proper (not Gδ)-subspace. This example shows that the class of all normal spaces which are topologically finite with respect to the class of all their proper Gδ-subspaces does not coincide with the class of all normal topologically finite spaces.
MSC: 54F45
Received: 2015-7-22
Accepted: 2015-9-12
Published Online: 2015-11-4
Published in Print: 2015-12-1
© 2016 by De Gruyter
