Various convergences of multifunctions. (English) Zbl 1497.54020
Summary: In the present paper, we introduce different types of convergences of nets of multifunctions from one topological space to another and compare them. Attempt has been made to formulate sufficient conditions under which these convergences preserve slight \(B^\ast\)-continuity of the limit multifunction.
MSC:
| 54C60 | Set-valued maps in general topology |
| 54A20 | Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) |
| 54C08 | Weak and generalized continuity |
| 54C10 | Special maps on topological spaces (open, closed, perfect, etc.) |
| 54D20 | Noncompact covering properties (paracompact, Lindelöf, etc.) |
| 40A30 | Convergence and divergence of series and sequences of functions |
Keywords:
\(\tau_{cl}^+\)-pointwise convergence; \(\tau_{cl}^-\)-pointwise convergence; \(cl\)-convergence; nearly-strong convergernceReferences:
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