Many people around the world are suffering from the climate changes due to the non respect of the whole ecological system. The need of taking into account the characteristics of environment when planning and acting in all the daily-life’ situations have become more and more important. Additionally, nowadays the protection of the environment is also one important need of humankind. In this perspective, many people are aware of the necessity to reduce the gap between human activities and the whole ecological system when even building or planning. Concerning the issue of harmony with the environment, more and more people around the world are interested in the problem of building or constructing houses in connection with the environment. Building techniques and of building construction materials suitable to the environment are used more often in many countries. Given the increasing human need of reducing the gap between human activities and the environment and given the increasing human need of improving the way of resolving the housing problem in the world, how can we introduce the principle of isomorphism so as to solve or to prevent such architectural problems? How can we define the principle of isomorphism in architecture? What are the main aspects of the principle of isomorphism in architecture? Referring to the problem situation to be solved, from which aspects of the principle of isomorphism in architecture, appropriate explanation and changes could be stated and realized in order to improve the situation? These are the questions examined in this piece of research.

A four part analysis
This work, whose main objective is to state the understanding and the extension of the principle of isomorphism in architecture from the analysis of the concept of isomorphism in some sciences, is made up of four parts. After the introduction, the theoretical framework, then the methodological aspects, later on, the results and finally the conclusion are presented.

Theoretical framework
The concept of isomorphism in some sciences The concept of isomorphism The definition of the notion of isomorphism has changed. In the past, the extension of the general notion of isomorphism was made up of many concepts such as: similarity (similitude) which implies making precise the accord between different branchs of a field of study or a discipline such as mathematics. Additionally, the link between isomorphism and structure was one of the characteristics of an isomorphism. It was admitted from research done in this domain that every structure carried within itself, a notion of isomorphism. Nowadays, and according to Timmermans (2012, p. 42), A homomorphism Ф A1→A2 is a mapping from A1 to A2 that preserves the structure relations in A1 (…); if a homomorphism Ф is one-to-one, onto and if its inverse mapping Ф-1: A2→A1 is also a homomorphism, then Ф is called an isomorphism. A homomorphism from A1 to itself is called an endomorphism. If this endomorphism is also an isomorphism, it is called an automorphism. In mathematics, the word derives from the Greek ‘iso’ which means «equal» and ‘morphosis’ meaning «to form» or «to shape». Isomorphism, in modern algebra according to William Hosch (2016), is a one-to-one correspondence (mapping) between 2 sets that preserve binary relationships between elements of the sets. Given that A&B are sets with elements an and bm, respectively. and indicate their respective binary operations, 2 vectors spaces V and W over the same field F are said to be isomorphic if there is a bijection T:V→ W which preserves addition and scalar multiplication, that is , for all vectors u and v in V, and all scalars c ∈ F, T(u+v) = T(u)+T(v) and T(cv) = cT(v) The correspondence T is then called an isomorphism of vector spaces. In Biology, the concept of isomorphism is related to similarity of form or structure between organism with independent ancestries; similarity in form, as in organisms of different ancestry; similarity of form, as in different generations of the same life cycle; similarity in the form or structure of organisms that belong to a different species or genus4.

In Chemistry Isomorphism is the existence of two or more substances that have the same crystal structure, so that they form solid solutions; a close similarity in the crystalline structure of two or more substances of similar chemical composition; the similarity in the crystal structures of similar chemical compounds; the existence of two or more different substances in the same crystal form and structure; an identity or close similarity in the crystalline form of substances usually containing different which operate on any 2 elements from a set and may be different. If there exists a mapping f such that f (aj ak) = f (aj ak) and its inverse mapping ∫-1 such that f-1 (br bs) = f-1 (br) f-1 (bs) Then the sets are said to be isomorphic and f and its inverse are isomorphisms.

• One-to-one correspondence between the elements of 2 or more sets such as those of Arabic and Roman numerals and between the sum or products of the elements of the one sets of these sets and those of the equivalents elements of the other set or sets.
• A one-to-one relation onto the map between the sets which preserves the relations existing between elements in its domain1.
• A one-to-one correspondence between 2 mathematical systems sets, etc that preserves the basic operations, as the correspondence between binary numbers and decimal numbers, each a set of real numbers2.
• A one-to-one correspondence between the elements of sets such that the result of an operation on elements of one set corresponds to the result of the analogous operation on their images in the other set.

According to Joyce (2015)3, elements but having similar composition. Then, an isomorphism in other words implies bijective correspondence between the elements of both groups and between the products of these elements. Apart from mathematics, the concept of isomorphism is studied and used in other scientific disciplines (chemistry, biology...). In these scientific fields, the word isomorphic is not conceived and cannot be taken in rigorous sense, but it frequently indicates only a great analogy, similarities, correspondence… Extension of relations in an isomorphism As far as the relations in isomorphism are concerned, if taking into consideration the following conception of strict extension as stated by Jayaprasad & Johnson (2012), a “relation set R* is said to be the strict extension of R , if R* contains all relations in R and at least one relation other than those in R which is not derivable from the relations in R. we denote R ϹR* when R* is a strict extension of R* ”, The figure below represented is a set of notions behind the concept of isomorphism in sciences.
To be continued