Hey everyone I'm new to this forum. I'm trying to teach my self some topology but I have no one to ask questions to.

I'm reading Munkres (2000) Topology. Section 16 example 3 left me with a question.

Let I = (0,1]. The book states that the dictionary order topology on IxI is different from the subspace topology on IxI obtained from the dictionary order topology on RxR.

Munkres states that {1/2}x(1/2,1] is open on the subspace topology but not on the order topology. It appears to me that it is open on both topologies.