Product of Connected Spaces with respect to Box Topology

In this video, we provided an example that an infinite product of connected spaces need not be connected with respect to the Box Topology. However, the infinite product of connected space is connected in the Product Topology.

[leonardomartinez]

Hi sir.
If I consider my sets in the example you demonstrated as
A= { (zi)i∈N ∈X| ∃M <0 :zi≥M ∀i∈N} (Lower bounded sequences)
B= {(zi)i∈N∈X| ∄M <0 : zi≥M∀i∈N} (Sequences not bounded below)
R^w is not connected in the box topology?