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You are here		thehighergeometer.wordpress.com Small fun observation about finite topological spaces, and some challenges - theHigherGeometer
\|	\|	alanrendall.wordpress.com Compact convex subsets of Euclidean space \| Hydrobates	2.1 parsecs away Travel
\|	\|	In a previous post I discussed the Brouwer fixed point theorem and I mentioned the fact that it applies to any non-empty closed bounded convex subset of a Euclidean space, since a subset of this kind is homeomorphic to a closed ball in a Euclidean space. However I did not prove the latter statement. I...	2.1 parsecs away Travel
\|	\|	mikespivey.wordpress.com No Integer Solutions to a Mordell Equation \| A Narrow Margin	3.2 parsecs away Travel
\|	\|	Equations of the form $latex x^3 = y^2 + k$ are called Mordell equations. In this post we're going to prove that the equation $latex x^3 = y^2 -7$ has no integer solutions, using (with one exception) nothing more complicated than congruences. Theorem: There are no integer solutions to the equation $latex x^3 = y^2...	3.2 parsecs away Travel
\|	\|	dominiczypen.wordpress.com Generalizing the T_0 separation axiom \| Musings on general topology and orderings	1.3 parsecs away Travel
\|	\|	The starting point of this blog post is a slight reformulation of the $latex T_0$ separation axiom: A topological space $latex (X,\tau)$ is $latex T_0$ if for all $latex x\neq y\in X$ there is a set $latex U\in \tau$ such that $latex \{x,y\}\cap U \neq \emptyset \text{ and } \{x,y\}\not\subseteq U.$ Given a cardinal $latex...	1.3 parsecs away Travel
\|	\|	cardinalguzman.wordpress.com P7090541 \| Cardinal Guzman	4.6 parsecs away Travel
\|		Encyclopedia Miscellaneous - 'quality' blogging since August 2011	4.6 parsecs away Travel