Omnipresence means being everywhere all at once. It is contrasted most naturally with local presence/action, though many people think it also contrasts with transcendence.
In the sense of a mere logical construct, omnipresence may include being present in either, or both, of all-of-space or all-of-time: everywhere in space at a particular instant or finite duration of time, everywhen in time at a particular location of space, or everywhere in space at all times. The most basic construct of omnipresence is presence everywhere in space at all times.
Two kinds of omnipresence
There may, at first, seem to be exactly two kinds of things that logically can be omnipresent, and each in a different way: everything-other-than-God, and God-Himself-alone.
The totality of everything-other-than-God may seem, by definition, to be "omnipresent as itself". But, unless some kind of physical thing, whether a kind of matter or a physical 'law', is arbitrarily selected as uniquely omnipresent in that totality, then no particular kind of physical thing can be defined as uniquely omnipresent. And, if no particular kind of physical thing can be defined apart from all others as omnipresent, then no particular kind of physical thing can be defined as transcendent (since unique omnipresence is a kind of transcendence), and hence, the totality of everything-other-than-God cannot be defined as coherent-in-itself. And, finally, if the totality of everything-other-than-God cannot be defined as coherent-in-itself, then the totality of everything-other-than-God is an ‘omnipresence of incoherence’. So, unless some kind of physical thing is transcendently omnipresent, then the only option in favor of an ultimate coherence is a transcendent God who, by His very transcendence, is omnipresent.
But, if an indifferent physical thing alone is omnipresent within non-indifferent living creatures, then there is an 'omnipresence of a transcendent indifference', which allows any living creature to be justified in any thought or act by mere appeal to himself as the sole judge of himself. So, a transcendent omnipresence of an indifferent physical thing, apart from God, allows the 'pure individualism' of Ayn Rand, which is not to be confused with the individualism that exists in the initial state of a mutually accounted group of (fallen or unfallen) individuals.
Balancing omnipresence and transcendence
On the face of it, there seems to be a problem of balancing omnipresence with transcendence. This is because the rational creature has mainly a practical view of physics, and thus a practical view of God. If a physical thing is pictured in the rational creature's mind as most directly omnipresent, then the picture is one of an homogenous physical world made up of that one thing alone. But, since physical things are observed to vary both in substance and form, the only thing which is at first imagined to be omnipresent is a thing which is imagined to transcend particular substances and forms. But, at that point, there seems to be an effort to keep from being forced to one side or the other: to holding that something must be transcendent and thus precluding its omnipresence, or to holding that something must be omnipresent and thus precluding its transcendence, Deism and Pantheism respectively.
Deism is the view that God's transcendence precludes, or prevents, Him from interacting fully with His Creation. Pantheism, in its purest form, is the view that God's omnipresence prevents Him from actually being the Creator, such that the Creation is God, and that otherwise there is no God.
So, God must be both transcendent and omnipresent in order to be God. But, then, is God more transcendent that He is omnipresent? But, if we assume that God's transcendence and omnipresence are equally 'weighted', then, by what logical mechanisms might we see them as equally 'weighted'?
Equating omnipresence and transcendence
The belief of Pantheism may be the result of admitting the natural sense that God is omnipresent while rejecting, or else failing take into account, the sense that God is transcendent. Deism may be the result of believing in the transcendence of God while failing to see how God can actually be present in His Creation without being His Creation. In any case, there seems to be a dualistic view of God's omnipresence and God's transcendence: God's omnipresence is different from God's transcendence. So, there seems to be a need to balance them with respect to each other.
But, there may be at least one way to resolve the seeming conflict between God's omnipresence and God's transcendence: by allowing that the classical geometric point may actually exist.
The classical geometric point is any point in space which cannot be divided into smaller spaces. This means that this point, if it exists, actually has no space. It's simply there, everywhere, in all of space, and in all of matter. It takes up all of space without taking up any of it.
From a classical view of physics, such a point allows that all of space and matter is infinitely divisible. In any case, if there really does exist a true, space-less point, then that point can be thought of as a kind of 'doorway' between God and all of His Creation. God can, then, be transcendent in the same way that He is omnipresent. In other words, He doesn't need to have extended Himself in order to be omnipresent. He doesn't need to take your chair from you in order to be in your chair: He can be in your chair right along with you without forcing you to one side.
Omnipresence vs. Transcendence: Summary of the False Dichotomy
If matter is non-quantized, then omnipresence of transcendence exists, since a non-quantized matter presupposes an omnipresent zero-point (a zero-point is similar to the Singularity of Einstein's Big Bang cosmology). If, on the other hand, matter is quantized, then, by a similar route of logic to that of non-quantized matter, omnipresence of transcendence exists. The only frame of reference in which omnipresence and transcendence are mutually exclusive is in the frame of reference of our everyday common sense practical view of the 'simple substantiality of matter,' and the 'simple non-substantiality of space'.