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## Homework Statement

Show that the collection

[itex] \{ \{a\}\times(b,c) \subset \mathbb{R^2} |a,b,c \in \mathbb{R} \} [/itex]

of vertical intervals in the plane is a basis for a topology on [itex] \mathbb{R^2} [/itex]

## The Attempt at a Solution

My question is just really about (a)X(b,c)

am I just basically letting a varying across the real line and then just pairing it up

with all the points on that line. So at each vertical interval

it will be open interval going up and down from point a and starting at b and going up vertically to c.