Is space impermanent?

Of course space is impermanent! Just put an object in it and the space is gone!

Space is an impermanent thing, but uncompounded space is a permanent thing.

See here for the definition of uncompounded space and how it differs from the regular notion of space.

According to the Scriptures the universe is infinite in time and space. By infinite what is meant is the length, width or number of solar systems (lokadhātu) in the universe are infinite. Within that infinite space there are sections that consist of one billion solar systems are called “Thri Sahashri Loka Datu” (equivalent to a galaxy). Such unfathomable spaces are always explained by similes. One such is - If someone takes mustard seeds amount equal to the volume of Thri Sahashri Loka Datu (equivalent to a galaxy) and travel in one direction placing one seed on one solar system, the seeds will come to an end but not the universe.

Buddha has not refereed to space as impermanent or not, but all things within it are. All the worlds of the devas, and the Brahma worlds are found within this time and space. For instance the scriptures talk about realms of the gods of the base consisting of the infinity of space... realms of the gods of the base consisting of the infinity of consciousness... realms of the gods of the base consisting of nothingness...

All of us beings of all these diverse worlds, whatever we do in time and space is going to come to pass sooner or later, like a picture you draw with a stick in flowing water. But there is one realm outside of time and space, Nibbhana, that Buddha wants us to reach, where we find the deathless. Once you’ve found the Deathless it’s always there as it is beyond time and space.

A collection of 1000 solar systems are called “Sahashri Loka Dhatu” in the scriptures. A collection of 1,000,000 solar systems are called “Divi Sahashri Loka Dhatu”. The universe may not be impermanent (as there is no mention of it). Within it, the solar systems are born, gets destroyed and it will be made again. Such cycles are called “Maha Kalpa(great kalpa)”. Maha Kalpa are further divided: time of solar system formation ( Sanwatta Kalpa), time of existence (Sanwatta Sthayi Kalpa), time of destruction (Wiwatta kalpa) and time of emptiness (Wiwatta Sthayi Kalpa). The time intervals are termed “Asankya Kalpa”.

For further reading: http://www.gutenberg.us/articles/eng/Buddhist_cosmology

Consider that for something to be impermanent it must have some sort of arising.

Arising implies Cessation. Without arising, there can be no cessation.

So you tell me, does space arise? Or is it simply the unawareness of space that ceases?

At any rate, compassion is a much more profound topic to put your efforts toward, for "the view of emptiness without compassion shall not lead you onto the sublime path" ~ Saraha

Space is not unconditioned. For example, there is space in the nostrils & ears. But if that space is filled up, with wax, snot or earplugs, the space disappears. This shows space is not unconditioned. The space is dependent & impermanent. To quote:

And what is the space property? The space property may be either internal or external. What is the internal space property? Anything internal, belonging to oneself, that's space, spatial & sustained: the holes of the ears, the nostrils, the mouth, the [passage] whereby what is eaten, drunk, consumed, & tasted gets swallowed, and where it collects, and whereby it is excreted from below, or anything else internal, within oneself, that's space, spatial, & sustained: This is called the internal space property.

MN 62

In Buddhism is explained immaterial meditative absorptions (arupa jhana), such as the dimensions of space, infinite consciousness & nothingness. Many 'Buddhists' (particularly Mahayana fixated on non-conceptuality/non-thinking) mistake these for the unconditioned Nirvana.

Nirvana, the Unconditioned, is the destruction of greed, hatred & delusion and is permanent for the arahant. Therefore, if an arahant thinks or speaks, the mind can no longer abide in the arupa jhana of the dimension of space however the mind continues to abide in Nirvana because an arahant can think & speak without greed, hatred & delusion.

This simple fact shows why space is not the unconditioned & why non-thinking is not Nirvana.

According to Buddhism, everything(except nibbana) is subject to causality(Sankatha) and everything arises dependently (Paticcasamuppanna) and there is no exception to space and time!

In the Pali Canon, the term Aggregate(Skandha) is defined as follows;

"To what extent does the designation 'aggregate' apply to the aggregates?"

"Monk, whatever form is past, future, or present; internal or external; blatant or subtle; common or sublime; far or near: that is called the aggregate of form. Whatever feeling is past, future, or present; internal or external; blatant or subtle; common or sublime; far or near: that is called the aggregate of feeling. Whatever perception is past, future, or present; internal or external; blatant or subtle; common or sublime; far or near: that is called the aggregate of perception. Whatever fabrications are past, future, or present; internal or external; blatant or subtle; common or sublime; far or near: those are called the aggregate of fabrication. Whatever consciousness is past, future, or present; internal or external; blatant or subtle; common or sublime; far or near: that is called the aggregate of consciousness. This is the extent to which the term 'aggregate' applies to the aggregates." Maha-punnama Sutta (MN 109)

So in a nutshell; aggravate means the delusion of existence(of Rupa, Vedana, Sanna, Sankhara and Vinnana) in time and space.

In Seela Sutta (SN 22.122) Ven. Maha Kotthita asks from Ven. Sariputta

"Sariputta my friend, which things should a virtuous monk attend to in an appropriate way?"

Ven. Sariputta replies;

"A virtuous monk, Kotthita my friend, should attend in an appropriate way to the five clinging-aggregates as

1. Inconstant(Aniccato)
2. Stressful(Dukkhato)
3. A disease(Roghato)
4. A cancer(Gandato)
5. An arrow(Sallato)
6. Painful(Aghato)
7. An affliction(Abadato)
8. Alien (Parato)
9. A dissolution(Palokato)
10. An emptiness(Sunnato)
11. Not-self (Anattato)

Which five? Form as a clinging-aggregate, feeling... perception... fabrications... consciousness as a clinging-aggregate. A virtuous monk should attend in an appropriate way to these five clinging-aggregates as inconstant, stressful, a disease, a cancer, an arrow, painful, an affliction, alien, a dissolution, an emptiness, not-self. For it is possible that a virtuous monk, attending in an appropriate way to these five clinging-aggregates as inconstant... not-self, would realize the fruit of stream-entry."

No one done a physics answer yet?

Here it is.

Space is impermanent. General relativity shows that space and time are linked together and they change with mass. Mass tells spacetime how to bend, spacetime tells mass how to move.

The whole field of cosmology studies how the space of universes changes.