## Semilocal connectedness of product spaces and $$s$$-continuity of maps.(English)Zbl 0982.54023

Summary: We consider the problem of the transfer of semilocal connectedness from factors to the product space and vice versa. Some sufficient conditions are given under which the product of semilocally connected spaces is semilocally connnected. The obtained theorems are not invertible, suitable examples are given.

### MSC:

 54D05 Connected and locally connected spaces (general aspects) 54B10 Product spaces in general topology 54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of topologies) 54C60 Set-valued maps in general topology

### Keywords:

semilocally connected spaces
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