Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/3892

 Title: Some Remarks on a Theorem of H.-J. Schmidt Authors: Barov, StoyuDimov, GeorgeNedev, Stoyan Keywords: Department of Topologyhyperspacesupper semi-finite topologyHS-spacesF-normal spacesK-, K’-, K’’- and K*-spacescontinuous mapsclosed mapsT2-, 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] URI: http://hdl.handle.net/10525/3892 Appears in Collections: Preprints

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