12 verses on Om
4-th verse of Mandukya Upanishad
4: Svapna-sthano’ntah-prajnah saptanga ekonavimsatimukhah praviviktabhuk taijaso dvitiyah padah
Second is Dreaming / Subtle: The second aspect of Atman is the Self in
the Dreaming state, Taijasa. In this second state, consciousness is
turned towards the inner world. It also operates through seven
instruments and nineteen channels, which engage the subtle objects of
the mental realm.
In dreaming states, we often see spaces that resemble to infinite universe. There could be pots and walls in the dream too that seem very real and cause division of spaces. Similarly, we see multiple people who appear to act independently too.
But here space (dreaming space) itself is not actually one before division. It was
there spanning wide. The difference of "here" and "there" was still
there in space. What ever the difference was already there was only
made apparent by pot and walls. If space had no difference within
itself or Svagatha Bheda, these separating agents would not be able to
create a difference. Just like you can't create a difference inside an
subatomic particle like electron. It is not divisible further. So this
example of Brahman being divided like space by separating entities is
not quite accurate.
This answers the question too.
As declared by Mandukya Upanishad 6th verse
6: Esha sarvesvara esha sarvajna esho’ntaryamy-esha yonih sarvasya
prabhavapyayau hi bhutanam
Find the Experiencer: The one who experiences all of these states of
consciousness is the omniscient, indwelling source and director of
all. This one is the womb out of which all of the other emerges. All
things originate from and dissolve back into this source.
Both dreaming state and waking state from the perspective of the experiencer is unreal. The only thing - the self that experiences this is real, according to Advaita Vedanta.
Taittiriya Upanishad
According to the definition of Brahman from Taittiriya Upanishad, a Brahman MUST be limitless/infinite:
As already known to you, brahman must have no limitations on attributes (or objects), time, or space. The differences such as here and there in spaces are appearances to us from our sense organs through Maya. In the dream, just as these appearances of space are created due to ignorance, similarly independently the appearance of space is created in the real world too, but the self (brahman) is the sole cause of getting deluded via sense organs and limiting the Brahman via space. Once the person gets enlightened, he knows that he is Brahman, hence totally beyond the concepts of space-time.
Note: I see that you are getting confused by the terms of Mithia (unreal) and false.
In Quantum Mechanics, there's a popular paradox called, Schrodinger's cat paradox.
In the thought experiment, a hypothetical cat may be considered
simultaneously both alive and dead, while it is unobserved in a closed
box, as a result of its fate being linked to a random subatomic event
that may or may not occur. This thought experiment was devised by
physicist Erwin Schrödinger in 1935[1] in a discussion with Albert
Einstein[2] to illustrate what Schrödinger saw as the problems of the
Copenhagen interpretation of quantum mechanics.
Src: https://en.wikipedia.org/wiki/Schr%C3%B6dinger%27s_cat
A cat called to be called - both dead and alive, until it is observed. This is a popular phenomenon, in Quantum Mechanics, where a probability observation of a physical feature of a state of the particle is both n and 1-n, till observation is made. For example, if the particle has a probability to be at point A at 50%, and at point B at 50%, it is supposed to be 50% at both points, until final observations are made.
The same is true for Advaita Vedanta, any observation at time t and space x could be both true or false until the final observation is made with consciousness. The very nature of appearances brahman through maya to be very uncertain is what makes it unreal or mithia which is not equivalent to false (which is established after observations of chit or consciousness).
PS - Erwin Schrodinger was a staunch Advait and used to read a lot of Upanishads in Sanskrit during his leisure time. Thanks to Swami Vivekananda for propounding the very philosophy in the West. Although this concept of mithia isn't much explored by Advaitas (the best ones I've seen are in a book called AdvaitaSiddhi) Quantum Mechanics has come up with a range of interpretations - Copenhagen, many worlds (or multiverses), Bohr's interpretation, Ensemble interpretation, etc.