"there corresponds" is a correct and usable phrase in written English.
It is typically used to convey that something aligns or matches with something else. Example: In this equation, each variable on the left side corresponds with a term on the right side, allowing us to solve for the unknown.
Our criterion yields examples illustrating pathology and also shows that to each equivalence class of idempotents there corresponds a "dimension function" from β × β into N ∪.
In particular, to every number β of Λ, different from its possible maximum, there corresponds the smallest element in Λ that is greater than β.
Generalising this idea we say that to every subset A of a system's phase space there corresponds a property PA so that the system possesses that property at time t iff the system's state x is in A at t.
That is, the key to his program is that for every word in the dictionary and every sentence in the language there corresponds a unique predicate that is true of just the tokens of that word/that sentence.
Formations are contents that enter into consciousness through carrying out specific functions in the sense that to every class and subclass of acts there corresponds a certain content specific to each and every act.
We say that a semi-inner-product is defined on, if to any there corresponds a real number denoted by satisfying the following properties: (s1) for, (s2) for, and, (s3) for, (s4).
Weights are given by the parameters wj (see equations following eq. (1)), which denote the relative strength of the modified synapses with respect to the baseline, to which there corresponds the value 〈w〉 = 1.
To each of these stochastic processes there corresponds a probability function, each of which, in turn, has a natural interpretation within the framework of Bayesian inference.
It is known that to every Mersenne prime there corresponds an even perfect number and vice versa.
But, as has been previously shown, sets cannot be piles of physical stuff or at any rate, when mathematicians talk about sets, they are not talking about physical piles because it follows from the principles of set theory that for every physical pile, there corresponds infinitely many sets.
there corresponds an -tuple such that (22).
