avoiding underlined spaces between two lines

Question

It must be very simple to get rid of but I could not find something addressing the problem : I would like to avoid underlined spaces between two lines. The following screenshot illustrates the problem in an org itemize:

I use the classic default-fill-column of 80.

The describe-char value of the space character (in place of the red cursor) gives the following:

 position: 500 of 1353 (37%), column: 0
        character: SPC (displayed as SPC) (codepoint 32, #o40, #x20)
preferred charset: ascii (ASCII (ISO646 IRV))
code point in charset: 0x20
           script: latin
           syntax:          which means: whitespace
         category: .:Base, a:ASCII, l:Latin
         to input: type "C-x 8 RET HEX-CODEPOINT" or "C-x 8 RET NAME"
      buffer code: #x20
        file code: #x20 (encoded by coding system utf-8-unix)
          display: terminal code #x20

Character code properties: customize what to show
  name: SPACE
  general-category: Zs (Separator, Space)
  decomposition: (32) (' ')

There are text properties here:
  face                 org-link
  font-lock-multiline  t
  fontified            t
  help-echo            [Show]
  keymap               [Show]
  mouse-face           highlight

EDIT (by Tobias): Org-text for reproduction:

- Energy and Numerical Weather Predictin; aussi ce papier sur [[http://web.mit.edu/lorenzcenter/about/LorenzPubs/The_Statistical_Prediction_of_Solutions_1962.pdf][statistic
  prediction of sol of dynamics equations]]

Local Variables:
fill-column: 80
org-hide-emphasis-markers: t
eval: (progn (setq org-descriptive-links nil) (org-toggle-link-display))
End:

Answer 1

Putting the following lisp-snippet into your initialization file (e.g., ~/.emacs) should do the job.

It puts a fontification rule at the very end of the org-specific font-lock-keywords. This rule clears underlining of spaces at line-beginnings by overriding the faces there.

(defface org-dont-underline-indents '((t :underline nil))
  "Avoid underlining of indentation.")

(defun org-dont-underline-indents ()
  "Remove underlining at indents."
  (add-to-list 'org-font-lock-extra-keywords '("^[[:space:]]+" 0 'org-dont-underline-indents t) 'append))

(add-hook 'org-font-lock-set-keywords-hook #'org-dont-underline-indents 'append)

The above version is greedy in the sense that it adds the org-dont-underline-indents face to all (non-empty) indents.

If this has any negative consequences I am not aware of yet you can use the following version that only adds the org-dont-underline-indents face if it finds some other face at the beginning of the indent.

(defface org-dont-underline-indents '((t :underline nil))
  "Avoid underlining of indentation.")

(defun org-search-underlined-indents (limit)
  "Match function for `org-dont-underline-indents'."
  (let (ret face)
    (while (and (setq ret (re-search-forward "^[[:space:]]+" limit t))
        (or (null (setq face (plist-get (text-properties-at (match-beginning 0)) 'face)))
            (eq face 'org-dont-underline-indents))))
    ret))

(defun org-dont-underline-indents ()
  "Remove underlining at indents."
  (add-to-list 'org-font-lock-extra-keywords '(org-search-underlined-indents 0 'org-dont-underline-indents t) 'append))

(add-hook 'org-font-lock-set-keywords-hook #'org-dont-underline-indents 'append)