Topology

The contents in the topology blog reflect my own tastes and interests in topology. Naturally, I write about topics that I find interesting.

The blog covers basic notions such as compact spaces, normal spaces, separable spaces, Lindelof spaces, paracompact spaces and metrizable spaces (or metric spaces), just to name a few. It also covers many classic examples of topological spaces such as Sorgenfrey line, Michael line, the square with the lexicographic order, double arrow space, first uncountable ordinal and tangent disk space, among others, as well as the more advanced examples such as Bing’s Example G, Bing’s Example H and Dowker spaces.

The notion of creating new spaces from old is also an important part of the contents. Thus subspace topology, quotient spaces, product spaces, function spaces and $\Sigma$-products and other topological structures are amply discussed throughout the blog.

Naturally extending basic notions is a favorite topic. For example, going from compact to countably compact and other notions of compactness such as sequentially compact, going from paracompact to countably paracompact and going from first countable spaces to Frechet spaces, sequential spaces, countably tight spaces, and k-spaces. For any topology course that is non-metric centric, transitioning from basic notions to these generalizations is an important part of the learning process. The blog aims to provide contents in great quantities for this transition.

I also like to write about well known results that are used in the literature. Often times, authors simply state the well known results in proving the theorems (sometimes even providing no references). These folklore results may indeed be well known for researchers, but may not be well known to students learning the subject. As I read papers of interests to me, I am always on the look out for folklore results as topics for my writing.

The blog should have something for everyone, for students taking courses in first year topology as well as working topologists looking for information.

This link will take you directly to the blog.

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$\copyright$ 2017-2018 – Dan Ma