Recent content by Kevin_H

Given the two systems below for an ##m \times n## matrix ##A##: (Sy 1): ##Ax = 0, x \geq 0, x \neq 0## (Sy 2): ##A^Ty > 0 ## I seek to prove: (Sy 1) is consistent ##\Leftrightarrow## (Sy 2) is inconsistent. I figured out how to prove Q ##\Rightarrow ## P by proving the contrapositive...

During lecture, the professor gave us a theorem he wants us to prove on our own before he goes over the theorem in lecture. Theorem: Let ##V_1, V_2, ... V_n## be subspaces of a vector space ##V##. Then the following statements are equivalent. ##W=\sum V_i## is a direct sum. Decomposition of...

Thank You very much for the feedback. I was originally thinking of approaching it that way, but I wasn't sure if I was allowed to assume the closure had an open subset containing ##x##. Now that I know, I can assume both ##\overline{U}## and ##\overline{V}## have open neighborhoods containing...

The book I am using for my Introduction to Topology course is Principles of Topology by Fred H. Croom. We are going over separation axioms in class when we were asked to prove that every Urysohn Space is a Hausdorff. What I understand: A space ##X## is Urysohn space provided whenever for any...

The book I am using for my Introduction to Topology course is Principles of Topology by Fred H. Croom. Problem: Prove that if ##X=X_1\times X_2## is a product space, then the first coordinate projection is a quotient map. What I understand: Let ##X## be a finite product space and ##...

Nice to meet you all. My name is Kevin and I am a undergraduate student pursuing a bachelors of science in mathematics. Next fall, I will be going to graduate school to pursue my masters in applied mathematics. My interest are anything involving math, physics, biology, and programming...