Given a topological space in which the operation of closure of a set, here denoted by 'e', has the properties: e (A+B) = eA+eB; A is a subset of eA, eO = 0, e2A = eA (where A is any subset of the space and 0 is the null set), we may define the interior 'i' of a set A by the formula iA = cecA (where cA denotes the complement of A in the space) and write a formula entirely equivalent to one due to C. Kuratowski (Fundamenta Mathematicae, III (1922), p. 183) in the following way: (1) (ei)2A = eiA.
Proceedings of the Iowa Academy of Science
©1941 Iowa Academy of Science, Inc.
Chittenden, E. W.
"A New Proof of a Formula of Kuratowski,"
Proceedings of the Iowa Academy of Science, 48(1), 299-300.
Available at: https://scholarworks.uni.edu/pias/vol48/iss1/73