The Hurewicz homomorphism and numerical forms

The Hurewicz Theorem

The fundamental group and homology groups both give extremely useful information, particularly about path-connected spaces. Both can be considered as functors, so we can use these constructional invariants as convenient guides to classifying spaces. However, though homology groups are often easy to compute, the fundamental group sometimes is not. In fact, it is often not even obvious when a spa...

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

Selective Screenability and the Hurewicz Property

We characterize the Hurewicz covering property in metrizable spaces in terms of properties of the metrics of the space Theorem 1. Then we show that a weak version of selective screenability, when combined with the Hurewicz property, implies selective screenability Theorem 4. 1. Definitions and notation Let X be topological space. We shall use the notation O to denote the collection of all open ...

A Functional Characterization of the Hurewicz Property

For a Tychonoff space $X$, we denote by $C_p(X)$ the space of all real-valued continuous functions on $X$ with the topology of pointwise convergence.  We study a functional characterization of the covering property of Hurewicz.

Numerical Continuation , and Computation Ofnormal Forms