Another View of the Weierstrass Theorem

The Theorem of Weierstrass

The basic purpose of this article is to prove the important Weier-strass' theorem which states that a real valued continuous function f on a topological space T assumes a maximum and a minimum value on the compact subset S of T , i.e., there exist points x1, x2 of T being elements of S, such that f(x1) and f(x2) are the supremum and the innmum, respectively, of f(S), which is the image of S und...

The Stone-weierstrass Theorem

The really new thing about Stone’s approach to the approximation theorem was the approach via lattices of continuous functions, although Lebesgue had noticed the importance of approximating the absolute-value function earlier. There is a segment of the mathematical community formed of people who are as likely to encounter a lattice in their work as an algebra and for whom the lattice version of...

Another proof of Banaschewski's surjection theorem

We present a new proof of Banaschewski's theorem stating that the completion lift of a uniform surjection is a surjection. The new procedure allows to extend the fact (and, similarly, the related theorem on closed uniform sublocales of complete uniform frames) to quasi-uniformities ("not necessarily symmetric uniformities"). Further, we show how a (regular) Cauchy point on a closed uniform subl...

A study on the definitions of religion from another view

Another View of the Classical Problem of Comparing Two Probabilities

The usual calculation of the P-value for the classical problem of‎ ‎comparing probabilities is not always accurate‎. ‎This‎ ‎issue arose in the context of a legal dispute which depended on when‎ ‎some written material was written in a diary‎. ‎The problem raises‎ ‎some issues on the foundations of statistical inference.‎