On generalized Blumberg sets.

*(English)*Zbl 0639.54011
Abstract analysis, Proc. 14th Winter Sch., Srnî/Czech. 1986, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 14, 399-405 (1987).

[For the entire collection see Zbl 0627.00012.]

The author studies Blumberg sets for multi-valued functions generalizing some of the results of C. J. Neugebauer, the reviewer, and himself. Similarly as it is done for single-valued functions, Blumberg sets play an important role in the description of certain quasi-continuous multivalued functions such as e.g., upper (lower) quasi-continuous. The author introduces quasi-Blumberg sets so that some of his results can be stated in a more natural way. Multi-valued somewhat continuity is defined and certain “almost” Blumberg sets are used in its description. An interested reader will surely look at closely related results contained in the paper by the author and T. Sǎlát, “Some generalization of the notion of continuity and Blumberg set of functions” (to appear).

{Reviewer’s remark: Several omissions of mathematical signs by the publisher, especially in the proof of Theorem 3, should not, by any means lower the value of this interesting article.}

The author studies Blumberg sets for multi-valued functions generalizing some of the results of C. J. Neugebauer, the reviewer, and himself. Similarly as it is done for single-valued functions, Blumberg sets play an important role in the description of certain quasi-continuous multivalued functions such as e.g., upper (lower) quasi-continuous. The author introduces quasi-Blumberg sets so that some of his results can be stated in a more natural way. Multi-valued somewhat continuity is defined and certain “almost” Blumberg sets are used in its description. An interested reader will surely look at closely related results contained in the paper by the author and T. Sǎlát, “Some generalization of the notion of continuity and Blumberg set of functions” (to appear).

{Reviewer’s remark: Several omissions of mathematical signs by the publisher, especially in the proof of Theorem 3, should not, by any means lower the value of this interesting article.}

Reviewer: Z.Piotrowski

##### MSC:

54C30 | Real-valued functions in general topology |

26E25 | Set-valued functions |

54C60 | Set-valued maps in general topology |