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Title: Some Remarks on a Theorem of H.-J. Schmidt
Authors: Barov, Stoyu
Dimov, George
Nedev, Stoyan
Keywords: Department of Topology
upper semi-finite topology
F-normal spaces
K-, K’-, K’’- and K*-spaces
continuous maps
closed maps
T2-, T3- and T4-spaces
Issue Date: Jul-1993
Publisher: Institute of Mathematics with Computer Center at the Bulgarian Academy of Sciences
Series/Report no.: 1993;7
Abstract: On the basis of a property of the hyperspace, H.-J. Schmidt [S] introduced implicitly a class of spaces called in the present paper HS-spaces. In [S, Theorem 11(3d)] it is stated that every Hausdorff HS-space is regular. Later on M. Paoli and E. Ripoli noted in [PR1] that the proof of the above assertion is incorrect, but the question of the correctness of the statement is open. We give a partial solution of this problem introducing a large class of spaces, which contains all Hausdorff spaces with countable character, where the theorem holds. Two reduction theorems are obtained as well. 1991 AMS Subj. Class.: primary – 54B20, 54CO5, 54D10, 54D15; secondary – 54B05, 54C10, 54G99.
Description: [Barov Stoyu; Баров Стою]; [Dimov George; Димов Георги]; [Nedev Stoyan; Недев Стоян]
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