As an alternative to the Khalimsky topology, the topology w on the digital plane Z2 was introduced by the author of this note who also proved a Jordan curve theorem for it. In the present paper, another Jordan curve theorem for the topology w is proved determining a large variety of Jordan curves in the topological space (Z2, w).

Pseudo-Riemannian manifolds of balanced signature which are both spacelike and timelike Jordan Osserman nilpotent of order 2 and of order 3 have been constructed previously. In this short note, we shall construct pseudo-Riemannian manifolds of signature (2s, s) for any s ≥ 2 which are spacelike Jordan Osserman nilpotent of order 3 but which are not timelike Jordan Osserman. Our example and tech...

In this paper, we investigate the generalized Hyers-Ulam stability of Jordan homomorphisms in Jordan Banach algebras for the functional equation begin{align*} sum_{k=2}^n sum_{i_1=2}^ksum_{i_2=i_{1}+1}^{k+1}cdotssum_{i_n-k+1=i_{n-k}+1}^n fleft(sum_{i=1,i not=i_{1},cdots ,i_{n-k+1}}^n x_{i}-sum_{r=1}^{n-k+1} x_{i_{r}}right) + fleft(sum_{i=1}^{n}x_{i}right)-2^{n-1} f(x_{1}) =0, end{align*} where ...