Recall that we consider epigroups as unary semigroups under the unary operation of pseudoinversion x |[right arrow] [bar.x].
Define a unary operation on H by the following rule: for all x [not equal to] 1 we set [bar.x] = 0, and [bar.1] = 1.
He suggested to consider words with not just one but countably many additional unary operations. In Section 3, we consider normal forms for Z-unary words and prove two of Zhil'tsov's propositions.
[perpendicular] : Q [right arrow] Q is a unary operation on Q, e [member of] Q.
1 : Q [right arrow] Q is an unary operation in Q, d [member of] Q.
Let Q be a unital quantale with a unary operation [perpendicular] satisfying the condition
In order to obtain the desired simplified axiomatic presentation of the category AFrm of approach frames, we introduce a finitely described subset F of the equations defining approach frames and then prove that any frame equipped with unary operations
[A.sub.[alpha]] and [S.sub.[alpha]], [alpha] [member of] [0, [infinity]], which satisfy the equations in F is in fact an approach frame.