Adding separators to categories (existing code)

I have this php code to display categories:

<span class="cat-links">
<?php
foreach((get_the_category()) as $category) {
    echo '<span id="'.$category->slug . '"><a href="' . get_category_link( $category->term_id ) . '" title="' . sprintf( __( "View all posts in %s" ), $category->name ) . '" ' . '>' . $category->name . '</a></span>'; $separator = ' ';
}

?>
</span>

I looked up the codex for get_the_category and it says $separator = ‘ ‘; would add a space between the categories. But wherever I place it even when using the ; symbols properly, it either does nothing or it loses the odd-colored tag with a different class in my example (test). I would appreciate all help or hints.

example: http://goldenred.web44.net/