Checking if user is logged in externally

<?php

if ( !is_user_logged_in() ) {

//not logged in

} else {

//is logged in

}
?>

But this is an external page so is_user_logged_in() is not yet a function

[moderated–bump removed. Please refrain from bumping as per Forum Rules]

Would normally point you to Integrating_WordPress_with_Your_Website, but since your requirement is “without including any files” then look at WordPress Cookies.

Related:
https://www.ads-software.com/extend/plugins/tags/authentication

How do I use these cookies to check if they are logged in?

Not sure but maybe these will help:
https://www.google.com/search?q=wordpress+cookies+for+login