I found a good solution to my problem. Using strpos() was not working for me but I did discover the correct wayt o detect spaces with a regular expression.
For future reference for anyone who may need it, the below expressions will look for spaces, lower case alphanumeric submissions without special chars:
if(ereg('[[:space:]]',$username) || ereg('[[:space:]]',$pass)){
#send message
$_SESSION["message"] = "User name and password can not contain spaces.";
#redirect
header("Location:mk_profile.php");
exit;
}
if(!ereg('^[a-z0-9]{3,15}$',$username)){
#send message
$_SESSION["message"] = "User name must only contain lower case letters and/or numbers, no spaces, and should be 3 to 15 characters in length.";
#redirect
header("Location:mk_profile.php");
exit;
}