A note on semitopological classes

A Note on Characteristic Classes

This paper studies the relationship between the sections and the Chern or Pontrjagin classes of a vector bundle by the theory of connection. Our results are natural generalizations of the Gauss-Bonnet Theorem.

A Note On Computing Set Overlap Classes

Let V be a finite set of n elements and F = {X1, X2, . . . , Xm} a family of m subsets of V. Two sets Xi and Xj of F overlap if Xi∩Xj 6= ∅, Xj \ Xi 6= ∅, and Xi \ Xj 6= ∅. Two sets X, Y ∈ F are in the same overlap class if there is a series X = X1, X2, . . . , Xk = Y of sets of F in which each XiXi+1 overlaps. In this note, we focus on efficiently identifying all overlap classes in O(n + ∑m i=1...

A Note on Culik-Yu Classes

Culik and Yu suggested a classification of cellular automata into four classes based on Wolfram's earlier heuristic classification. The purpose of this note is to determine the position of these classes within th e arithmetical hierarchy. We will show that CLASS ONE and C LASS T wo are rrg-complete whereas C LASS THREE is ~g­ complete . C LASS FOUR is tri vial.

A Note on Unambiguous Function Classes

A Note on Teaching for VC Classes

where we use c |X to denote the projection of c on X. The teaching dimension of C is the smallest number t such that every c ∈ C has a teaching set of size no more than t [GK95]. However, teaching dimension does not always capture the cooperation in teaching and learning, and the notion of recursive teaching dimension has been introduced and studied extensively in the literature [Kuh99, DSZ10, ...