send_core_update_notification_email example

// Only relax the filesystem checks when the update doesn't include new files.         $allow_relaxed_file_ownership = false;
        if ( 'core' === $type && isset( $item->new_files ) && ! $item->new_files ) {
            $allow_relaxed_file_ownership = true;
        }

        // If we can't do an auto core update, we may still be able to email the user.         if ( ! $skin->request_filesystem_credentials( false, $context, $allow_relaxed_file_ownership )
            || $this->is_vcs_checkout( $context )
        ) {
            if ( 'core' === $type ) {
                $this->send_core_update_notification_email( $item );
            }
            return false;
        }

        // Next up, is this an item we can update?         if ( 'core' === $type ) {
            $update = Core_Upgrader::should_update_to_version( $item->current );
        } elseif ( 'plugin' === $type || 'theme' === $type ) {
            $update = ! empty( $item->autoupdate );

            if ( ! $update && wp_is_auto_update_enabled_for_type( $type ) ) {