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Product of connected spaces

The product of any family of connected spaces is connected. For two factors, fix

y_{0}

and use the connected sets

(X \times {y_{0}}) \cup ({x} \times Y), x \in X .

They cover

X \times Y

and all contain the connected horizontal slice

X \times {y_{0}}

.

 Ancestors (5)

 Incoming links (1)

Solution