Chemical Reaction Topology Theory (I) Reaction Path Topology Space

A fundamental group π₁(F^-(A), K_o) can be formed according to the close homotopy reaction paths (σ(0)=σ(1)=K_o). Giving a subgroup Θ of π₁ (F^-(A), K_o) and reaction paths σ on F(A), we dsfine the following reaction path set,\mathrmP^(\ominus)=\left\\Theta\sigma \mid \Theta \subset \pi_1\left(F^-(A), K_0\right), \sigma(0)=k_0, \sigma(1) \in F^-(A)\right\
The map p is defined as p (Θσ)=σ(1)
It can be proved that the set\widetildeC(λ,i)forms the topology subbasis of P^Θ, here \widetildeC(λ,i) satisfies \widetildeC(λ,i)=Θσ|P(Θσ)∈C(λ,i) is the (λ,i)-thstructure on F^-(A)⁵
Therefore, the set P^(Θ) is proved to be a topology space which we call as reaction path topology space (RPTS). And what is more important is that (P^(Θ),p) is proved to be a covering space or the topology space F^-(A).
The homotopy reaction mechanism number (HRMN) betweem k_o and k of F^-(A) on the RPTS P^(Θ) is defined as the number of the set Θσ|σ0=k_o, It can be easily proved that the HRMN is all the same between any two points on F^-(A), and this number is equaled to the number of the set
Θ α|α∈π₁ (i>F^-(A),K_o)