Abstract
Algebraic properties of $n$-place opening operations on a fixed set are described. Conditions under which a Menger algebra of rank $n$ can be represented by $n$-place opening operations are found.
Highlights
It is known [5] that on the topology on a set A one can talk in the language of open sets, the language of closed sets, the language of interior operations, or the language of closure operations
A natural question is about a similar characterization of interior operations having applications in topology and economics
Kulik observed in [4] that the superposition of two interior operations is not always an interior operation and found conditions under which the composition of two interior operations of a given set A is an interior operation of this set. He proved that a semigroup S is isomorphic to a semigroup of interior operations of some set if and only if S is idempotent and commutative
Summary
It is known [5] that on the topology on a set A one can talk in the language of open sets, the language of closed sets, the language of interior operations ( called opening operations), or the language of closure operations. A natural question is about a similar characterization of interior operations having applications in topology and economics. Such operations were first studied from an algebraic point of view by Vagner [7]. Kulik observed in [4] that the superposition of two interior operations is not always an interior operation and found conditions under which the composition of two interior operations of a given set A is an interior operation of this set He proved that a semigroup S is isomorphic to a semigroup of interior operations of some set if and only if S is idempotent and commutative. We introduce the concept of n-place interior operations and find conditions under which a Menger algebra of rank n can be isomorphically represented by n-place interior operations of some set
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
