A checkbox is an array you can use either an indexed or associative array, I like touse the associative cause they are easier to understand and work with. This is what you have
<input type="checkbox" name="space" value="Ballroom" class="required" />
and this is what you need in the form to make an associative array.
<input type="checkbox" name="space[ballroom]" value="Ballroom" class="required" />
Then to access it you would use
$_POST['space'][ballroom]
and if it were checked the value would be Ballroom