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**On generalized continuous multifunctions and their selections.**
*(English)*
Zbl 1160.26001

The authors consider the notions of upper and lower \(\varepsilon\)-continuous multifunctions introduced earlier by M.
Matejdes [Tatra Mt. Math. Publ. 40, 81–89 (2008; Zbl 1199.54123)] where the author had taken a very general approach by defining the concepts with respect to a non-empty family of non-empty sets \(\varepsilon\). The authors particularly investigate the concept of \(\varepsilon\)-cluster multifunctions and their selections. They prove some results related to its continuity and prove that this function has a closed graph. They also investigate the properties of densely lower \(\varepsilon\)-continuous forms.

Reviewer: Pratulananda Das (Kolkata)

### MSC:

26A15 | Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable |

54C08 | Weak and generalized continuity |