There is famous Kołmogorov-Arnold theorem for continuous functions composition - continuous function of several variables can be composed of continuous functions of two variables.

Specialization of such theorem into smooth functions is false: there is no similar composition obeying smoothness - that is there are smooth functions of several variables that cannot be composed of smooth function of 2 variables.

Take a look here: Kolmogorov superposition for smooth functions

There is an obvious way around: generalization and even grand generalization.

Generalization: Is Kolmogorov-Arnold theorem true for just functions ( non-continuous)?

If above question is interesting we may ask for Grand Generalization: Let KA(f, X) means the following hypothesis: given object f of some class containing several variables ( function, relation, rules of inference etc), and characteristics X ( continuous, transitive etc) valid for such class of objects, is it possible to compose every object of class f as finite number of objects of the same class with 2 variables with the same characteristic X?

Is there something known for Grand Generalization K(f,X) for various f and X?

There is famous Kolmogorov-Arnold theorem for continuous functions composition - continuous function of several variables can be composed of continuous functions of two variables.

Specialization of such theorem into smooth functions is false: there is no similar composition obeying smoothness - that is there are smooth functions of several variables that cannot be composed of smooth function of 2 variables.

Take a look here: Kolmogorov superposition for smooth functions

There is an obvious way around: generalization and even grand generalization.

Generalization: Is Kolmogorov-Arnold theorem true for just functions ( non-continuous)?

If above question is interesting we may ask for Grand Generalization: Let KA(f, X) means the following hypothesis: given object f of some class containing several variables ( function, relation, rules of inference etc), and characteristics X ( continuous, transitive etc) valid for such class of objects, is it possible to compose every object of class f as finite number of objects of the same class with 2 variables with the same characteristic X?

Is there something known for Grand Generalization K(f,X) for various f and X?

There is famous Kołmogorov-Arnold theorem for continuous functions composition - continuous function of several variables can be composed of continuous functions of two variables.

Specialization of such theorem into smooth functions is false: there is no similar composition obeying smoothness - that is there are smooth function of several variables that cannot be at composed of smooth function of 2 variables.

Take a look here: Kolmogorov superposition for smooth functions

There is an obvious way around: generalization and even grand generalization.

Generalization: Is Kolmogorov-Arnold theorem true for just functions ( non-continuous)?

If above question is interesting we may ask for Grand Generalization: Let KA(f, X) means the following hypothesis: given object f of some class containing several variables ( function, relation, rules of inference etc), and characteristics X ( continuous, transitive etc) valid for such class of objects, is it possible to compose every object of class f as finite number of objects of the same class with 2 variables with the same characteristic X?

Is there something known for Grand Generalization K(f,X) for various f and X?

There is famous Kołmogorov-Arnold theorem for continuous functions composition - continuous function of several variables can be composed of continuous functions of two variables.

Specialization of such theorem into smooth functions is false: there is no similar composition obeying smoothness - that is there are smooth functions of several variables that cannot be composed of smooth function of 2 variables.

Take a look here: Kolmogorov superposition for smooth functions

There is an obvious way around: generalization and even grand generalization.

Generalization: Is Kolmogorov-Arnold theorem true for just functions ( non-continuous)?

If above question is interesting we may ask for Grand Generalization: Let KA(f, X) means the following hypothesis: given object f of some class containing several variables ( function, relation, rules of inference etc), and characteristics X ( continuous, transitive etc) valid for such class of objects, is it possible to compose every object of class f as finite number of objects of the same class with 2 variables with the same characteristic X?

Is there something known for Grand Generalization K(f,X) for various f and X?