- #1

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## Homework Statement

Here it is in all its glory: http://imgur.com/w08cp

## Homework Equations

Here is a definition on what an upper ideal is: http://imgur.com/ZILjW

Here's what a finite topological space is: http://imgur.com/tBGTn

## The Attempt at a Solution

From what I gather, I want to show that if [tex]B\in Ty[/tex], then the inverse image of B is an element of Tx.

From there I started by letting [tex]B\in Ty[/tex]. Ty is a topology on Y and it is the set of upper ideals in [tex](Y,\leq)[/tex]. Thus for [tex]b\in B\in Ty[/tex], and [tex]y \in Y[/tex], [tex]b \leq y[/tex] so [tex]y \in Ty[/tex].

But I'm not seeing it, I don't know how one definition gets me to another step. Was I even in the right track?