Advanced Knowledge Problem of the Week 4-12-18: Cofinite Topology Compactness [Topology]

Check out this Advanced Knowledge Problem of the Week.
Be sure to let us know how you solved it in the comments below or on social media!


Solution below.

Solution


Video


Comments

Post a Comment

Popular posts from this blog

Math History Youtube Mini-Series: The History of Greek Mathematics

Image
Mathematics has long been a unifying element across cultures around the globe. Beginning first as a tool used for counting and practical problems, Mathematics eventually came to be an intellectual interest producing theories and ideas that described the world. As one of the most pursued sciences, Math has built off itself creating new ideas on the backs of old ones. The study of Math history attempts to document and understand this path that Mathematics has taken from antiquity to now. Below you may watch this new mini-series on Math History which focuses on the breakthroughs made in the early years of Mathematics in Greece. This series is meant to be a short introduction to Math History and as such covers only part of the Mathematical discoveries of one culture. Greek mathematicians as a whole did much to learn from and expand upon the knowledge established by the civilizations before it. Yet, within this series we have left out many Mathematicians that were instrumental in the develo...
Read more

Some History and Unsolved Problems in Number Theory

Image
Number theory is a very old subject, which is concerned with the set of integers. Number theory started with the concept of integers and simple operations on the integers such as addition, subtraction, etc. Number theory of the greeks is primarily found in the works of Euclid and Plato. Indian mathematicians of antiquity such as Brahmagupta also made significant contributions (one of Brahmagupta's contributions was work on what is now known as Pell's equation). Pierre de Fermat was an important figure in number theory as well, he is responsible for Fermat's theorem as well as Fermat's Last Theorem (a problem which is now solved). Some additional major figures in early number theory were Leonhard Euler, Joseph-Louis Lagrange, and Carl Friedrich Gauss. Eventually number theory itself started to split into recognizable subbranches, two major ones being algebraic number theory and analytical number theory. Analytical number theory is concerned with the use of real and compl...
Read more