Math 762 Differential Topology

Course Notes for Math 753: Differential Forms and Algebraic Topology

A note on approximation conditions, standard triangularizability and a power set topology

The main result of this article is that for collections of entry-wise non-negative matrices the property of possessing a standard triangularization is stable under approximation. The methodology introduced to prove this result allows us to offer quick proofs of the corresponding results of [B. R. Yahaghi, Near triangularizability implies triangularizability, Canad. Math. Bull. 47, (2004), no. 2...

Uniform Continuity of the Value of Zero-Sum Games with Differential Information

We establish uniform continuity of the value for zero-sum games with differential information, when the distance between changing information fields of each player is measured by the Boylan pseudometric. We also show that the optimal strategy correspondence is upper semicontinuous when the information fields of players change (even with the weak topology on players’ strategy sets), and is appro...

The Tau-Collocation Method for Solving Nonlinear Integro-Differential Equations and Application of a Population Model

This paper presents a computational technique that called Tau-collocation method for the developed solution of non-linear integro-differential equations which involves a population model. To do this, the nonlinear integro-differential equations are transformed into a system of linear algebraic equations in matrix form without interpolation of non-poly-nomial terms of equations. Then, using coll...

Internal Topology on MI-groups

An MI-group is an algebraic structure based on a generalization of the concept of a monoid that satisfies the cancellation laws and is endowed with an invertible anti-automorphism representing inversion. In this paper, a topology is defined on an MI-group $G$ under which $G$ is  a topological MI-group. Then we will identify open, discrete and compact MI-subgroups. The connected components of th...