Q; if for the purpose of acquire knowledge without moving with mahram?
A; All-Praise is due to Allah,
It is not permissible for any female to travel anywhere weather its Hajj or somewhere else, It was narrated that Ibn 'Abbaas (may Allaah be pleased with him) said: The Prophet (peace and blessings of Allaah be upon him) said: “No woman should travel except with a mahram, and no man should enter upon a woman unless there is a mahram with her.” A man said: “O Messenger of Allaah, I want to go out with such and such an army, and my wife wants to go for Hajj.” He said: “Go for Hajj with her.” Narrated by al-Bukhaari (1763) and Muslim (1341).
Shaykh Muhammad bin Saalih al-`Uthaymeen said; If the woman does not have a Mahram, it is not obligatory upon her to perform Hajj. This means that either the obligation is removed from her due to the lack of ability to reach Makkah- and lack of ability is a legislated inability- or it is not obligatory upon her to perform it, meaning that if she dies whoever she leaves behind performs it for her. Anyway, I say to the questioner that the woman has not committed a sin if she dies without performing Hajj due to not having a Mahram. That does not harm her because she is excused and unable according to the religion. Indeed Allah, the Most High, said: And Hajj (pilgrimage to Makkah) to the House ( Kaýaba) is a duty that mankind owes to Allah, those who can find a way there.[Aal ýImran 97] End of quote.
(See Fatawa Islamiyah Darussalam Vol:4 p. 46)
Al-Nawawi (may Allaah have mercy on him) said in Sharh Saheeh Muslim, explaining that travel in this case is not defined by a specific distance: Everything that is called travelling, it is forbidden for a woman to do without her husband or a mahram, whether it is three days, two days or one day, or anything else, because of the hadeeth of Ibn ‘Abbaas, according to which the Prophet (peace and blessings of Allaah be upon him) said: “No woman should travel without a mahram.” This includes everything that is called travel. End quote.
And Allaah knows best...