Arrays Of Checkboxes

I have two related tables in my database. One stores events and the other stores a list of key topics.

I have an interface set up where users can add / edit events.

In the add event page, I am querying the "key topics" table and returning them as options (array of checkboxes). The user makes their pick, and submits. All the data saves in the 'event" table, including the primary id of the "topics".

That part works great. The problem I am having is when the EDIT event page resolves, I am trying to "check" the options that were previously saved.

First thing I do (at the top of the page) is to query the events table to pull all of the data out. I use the 'events" table to do this.

For the checkboxes, I am once again looping through them in a query that uses the "key topics" table. So the boxes are displayed, but I can't seem to get the logic right to have the appropriate ones checked. here is my current code: