The Gemara in Masechet Shabbat (5b) addresses the case of a person holding a Megila – a scroll of a book of Tanach – on a roof during Shabbat, and the Megila unravelled and now hangs alongside the wall of the building. In certain situations, the Gemara establishes, it would be forbidden to roll the Megila once it had unraveled and one end reached near the ground. (We will not discuss here the particular conditions in which this Halacha applies.) In such a case, the Gemara adds, the person should turn the Megila around so that the writing faces towards the wall. It would be degrading to the sacred text to leave it exposed until after Shabbat when one may then roll the Megila, and one should therefore turn the scroll around so that the writing faces the wall, rather than be exposed to public view.
The Ran (Rabbenu Nissim of Gerona, Spain, 1290-1380), in his commentary to Masechet Shabbat, writes that the rule established in this Talmudic passage applies to all Torah books. Namely, after one finishes studying from a Sefer (Torah book) he should not leave it open, as this would be undignified. He should rather make a point of closing the book. A number of later writers warned that leaving a Torah book open increases the chances of forgetting the material learned.
This is indeed the accepted practice, and one must therefore ensure not to leave a Torah book open when he is not studying from it. In fact, it is customary even when leaving the Bet Midrash (study hall) momentarily to close one's book or leave a tissue or paper over the pages, so that the text is not left exposed. Some people have the practice of closing the book and leaving the cover open as an indication that they intend to immediately return to resume their learning.
Summary: After a person finishes studying from a Torah book, and even if he takes a brief pause from his learning, he should make a point of closing the book or at least covering the text so it is not left exposed.
