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Connectedness and strong semi-continuity. (English) Zbl 0553.54005

This paper shows that connectedness is a topological property shared by any space and its \(\alpha\)-topology. By noting that an appropriate change of topology reduces strong semi-continuity to the usual notion of continuity, the paper shows that the preservation of connectedness by strong semi-continuous functions is a particular case of its preservation by continuous functions.

MSC:

54D05 Connected and locally connected spaces (general aspects)
54C08 Weak and generalized continuity
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