The Qur'an presents the precept of Tawhid as Allah being the sole Creator, the uncreated and the cherisher and sustainer of the worlds. Thus there are two precepts of Tawhid to be observed as the epistemological foundation of all Islamic socio-scientific order. These are first the Tawhidi Precept of Unity. This signifies the a priori, most irreducible and immutably axiomatic existence of Allah as the sole Creator and one who is not created. In the earlier chapters we have called this state of completeness of knowledge of the Supreme Creator as the Stock of Knowledge. We had also equated this primal premise with the complete knowledge embalmed in the event of Hereafter (Akhira). Hence in this primal state of the Precept of Unity we had shown that Creation incessantly springs from the Stock, wherein the following equivalence holds: Allah=Stock of Knowledge=Truth=Qur'an (Essence=Lauh Mahfuz)=Cumulative Stock of Knowledge in Akhira. In this way, the Precept of Unity as the immutable and pervasive springboard of creation bestowing meaning and form, becomes a mathematically closed mapping of Stock of Knowledge into itself through the process of creation cumulating in the same complete stock of knowledge in Akhira. In other words, the Precept of Unity is the axiomatic foundation of belief, which now assumes the meaning of knowing and certainty followed by advance in every facet of life and thought.

We must now inquire as to what consequences the universe would face if the divine origin of Tawhid as the primal epistemology of existence was not there. This is a mathematical ushering and such a course of comprehension of divine reality was taken up by the greatest minds in every age, both among Muslims and anon-Muslims and earlier still by the Greeks and in all of recorded history. The Qur'an says in this regard that Allah has invoked the truth of His existence both to the animate and inaimate worlds and that he has manifested His reality pervasively for all to seek. Many Qur'anic verses of these types that self-references the Qur'an and Allah as the true reality found the basis of Reality (Haqq ul-Yaqin). Thus there are now at least two premises of coherent correspondences that are found to emanate from the divine root of primal Unity -- the Precept of Unity. These are the first the question that we must now tackle although briefly here on the logical self-referencing of Allah in the Qur'an as the seat of all creation; secondly, the conjoint meaning Reality that emanates from the same self- referencing root of existence.

Let T denote Tawhid as a topology. The mathematical properties of a topology must characterize T as being a collection of all subspaces, say X, and endowed by a field or encompassing space, say t. Hence T=(X,t). Furthermore, t has the property that it includes both X and the nullity of X. All possible mathematical unions (denoted here by the symbol U) and mathematical intersections of all subspaces of T (denoted here by the symbol INT). There is just an additional characterization that must be included for T. That is of the possibility of infinite intersections, and hence of the possibility for infinite union of infinite intersections of subspaces of T. This additional property is in addition to the text book definition of a topological space with t as the topology of its subspaces.

First, we will define here the space X belonging to t as the space of all worlds that the Qur'an speaks about. Since Allah is the Lord of all the worlds and there are uncountable number of them, therefore, ??X must also belong to t for infinite unions of X's. Next we will define t as the Divine Laws held up as relations between knowledge and the worlds. Since t itself is also infinite in its capacity for generating relations, therefore, Ut belongs to t. As well as ??t for all possible t's belong to t. That is, U??t belongs to t. But since X and UX belong to t, therefore, (U INT X) belongs to t. t becomes the carrier of the Stock of Knowledge into the creation of material forms that are signified by X's.

In the limit of infinite possibilities for X's and t's through combinations and evolutions in them, the following relations must hold: lim{[U INT X(t)]/dt} > 0; X(t) here denotes the functional dependence of X on t because of the topological inclusions. Hence two dynamics are involved here. First lim[U INT t] comprehends the whole of T and along with this the positive mapping of t on X must also make lim[U INT X] comprehend the whole of all X's. In the limit therefore, intersections of infinitely limiting subspaces become the union of such subspaces. This is the meaning of irreducibility of T. T comprehends both the subspaces as well total space of X's and t's and interrelationships in these.

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