A topological space, whose underlying set has two elements, is called the Sierpinski-space if its topology is non-discrete and non-indiscrete. In this publication, we give a necessary and sufficient condition for the continuity of a characteristic function from a topological space into the Sierpinski-space. In fact, this is our solution to an exercise outlined in … Lire la suite de The characteristic function and the Sierpinski-space
Topology generated
All topologies on a set with two or three elements
A topology on a set X is a set O of subsets of X satisfying the following two conditions: firstly, every union of sets of O is a member of O; secondly, every finite intersection of sets of O belongs to O. A topology on X is thus a subset of the power set of … Lire la suite de All topologies on a set with two or three elements
Formalis Mathematica 