When Haruhi Suzumiya's emotions become unbalanced, closed space is created in a limited area as a way for her to release her anger and frustration through creatures called celestials. It is the duty of an 'Agency' esper to remove the celestials, which destroys the space.
Esper Itsuki Koizumi pointed out that Haruhi's depression does not cause closed space, only frustration. He asked Kyon to avoid doing anything which would trigger Haruhi to create closed space (in other words, keep her happy and entertained).
Koizumi believes that if the closed space is not shut down, reality can be permanently altered in the area, and believes that Haruhi may in fact have altered the entire world one or more times previously.
There are only three times in the series that Haruhi's closed spaces are shown to Kyon: once when Itsuki Koizumi shows him his powers as an esper, once when Kyon and Haruhi wake up in one at school (having seemingly been teleported there), and once when Kyon found himself in a combination between Haruhi and Sasaki's spaces, which were "at war" with one another. The second case was particularly unusual, as neither normally could enter closed space without esper assistance. Kyon went to sleep at his house but woke up at school, along with Haruhi. The space was different than normal; Koizumi was only able to enter when given power from the other espers, and even then could not last there long.
After Kyon resolved the school closed space situation by "calming" Haruhi's frustration, closed space occurred only rarely. The next incident occurred when Haruhi got frustrated by losing a baseball game, but it was resolved when the SOS Brigade pulled off an unlikely victory. Haruhi specifically did not create closed space after fighting with Kyon in The Sigh of Haruhi Suzumiya because she was feeling depression rather than anger.
Kyon professed not to care if Haruhi lost a video game duel during The Day of Sagittarius, saying she would need to learn her lesson one day. Koizumi took this as a sign that Kyon trusted her not to create closed space in such an eventuality.
After Haruhi met Sasaki during spring break, however, Haruhi began creating much closed space again because Sasaki introduced herself as Kyon's "close friend". However, the celestials did not attack, acting as if they were in a daze. The 'Agency' still opted to destroy them.
In the α timeline, the incidence of closed space decreased; Koizumi believed this was because Haruhi planned on adding first-year students to the Brigade, and had her mind on things other than Sasaki.
In the β timeline, they also decreased. Koizumi believed this was due to her worries over Nagato's illness. However, he was wary of making a mistake; the celestials could be marshaling their strength instead. Koizumi believed that avatars accelerated the process of creating sealed reality.
As the timelines merged, so did the two versions of closed space. Despite Haruhi's captivity at the hands of Fujiwara and Kuyou Suou, Haruhi's closed space still formed, as she had somehow "split" herself into two, with Yasumi Watahashi acting as Haruhi's "other half" and generating the closed space anyway.
Sasaki creates an alternate version of closed space, in which the world is entirely white or clear sepia/cream and it encloses the entire world, along with the fact that there are no celestials. However, they are devoid of any other change at all. Esper Kyouko Tachibana was able to show this to Kyon just by holding his hand. The two did a "spirit walk" around the space until they returned to their original positions. They had only held hands for ten seconds in the real world, but the trip seemed much longer.
As a Moments subpage, all spoilers are unmarked as per policy. You Have Been Warned.
The user can create a new reality which overlaps reality/space that already exists and become the god of their closed space. Closed spaces take in a number of elements from the real world and may only have a few differences, with such examples being the sky changing into a different color than normal or the presence of unearthly beings seemingly living within the closed space. The user can trap anyone who enters a closed space within their reality or restrict certain people from entering and leaving.
If someone were to enter a closed space from point A in the real world and traveled to point B within closed space, they would end up at the real-world version of point B. To any outsiders, it would seem as though they have somehow teleported. For example, if someone entered Closed Space while on top of a building then walked downstairs onto a parking lot and left Closed Space, they would end up in the real-world version of the parking lot in the exact same location. Since Closed Spaces are layers of the real world, any damage done to a Closed Space has the potential to also damage its real-world counterpart, and vice-versa. Usually, Closed Space cannot be seen from the outside, but it can be detected by people with special powers or other means.
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