Blogs about: Topology
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Euclidean Spaces
In light of our discussion of differentials, I want to make a point here that is usually glossed over in most treatments of multivariable calculus. In a very real sense, the sources and targets of our… more →
The Unapologetic Mathematician
A Note About Countably Compact Spaces
Dan Ma wrote 1 day ago: This is a discussion on several additional conditions that would turn a countably compact space into … more →
The Finite Intersection Property in Compact Spaces and Countably Compact Spaces
Dan Ma wrote 3 days ago: This is a discussion of a basic result about compact spaces, namely the characterization of compactn … more →
Irreducible components
Qiaochu Yuan wrote 4 days ago: If it wasn’t clear, in this discussion all rings are assumed commutative. Given a variety like … more →
Countably Compact Spaces with G-delta Diagonals
Dan Ma wrote 4 days ago: It is a classic result in general topology that any compact space with a diagonal is metrizable ([3] … more →
The Noetherian condition as compactness
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Qiaochu Yuan wrote 5 days ago: Let’s think more about what an abstract theory of unique factorization of primes has to look l … more →
Hairy Balls and Cyclones
Sunny wrote 6 days ago: There are other important properties of homology, such as excision, but before I delve into those, I … more →
Ψ-Spaces - spaces from almost disjoint families
Dan Ma wrote 6 days ago: As the title suggests the spaces are defined using almost disjoint families, in our case, of subsets … more →
Quick Stop @ SharePoint – Topology
arungopalv wrote 1 week ago: The entry point to a SharePoint site is Web Application also known as virtual server in earlier vers … more →
Spectra of rings of continuous functions
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Qiaochu Yuan wrote 1 week ago: An analyst thinks of the ring of polynomials as a useful tool because, on intervals, it is dense in … more →
Homotopy Invariance
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Sunny wrote 1 week ago: Continuing with properties of singular homology, I will now talk about the invariance of homology un … more →
Motives in Paris and Regulators in Barcelona
Andreas Holmstrom wrote 1 week ago: The Events page has been updated again. Some highlights: Copenhagen Topology Conference (Jan 8-10) C … more →
Perfect Image of Separable Metric Spaces
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Dan Ma wrote 1 week ago: In a previous post on countable network, it was shown that having a countable network is equivalent … more →
Functoriality of Homology
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Sunny wrote 1 week ago: Last time, I wrote about singular homology and how it describes topological spaces. Now, I’ll … more →
Metrization Theorems for Compact Spaces
Dan Ma wrote 1 week ago: In this blog I have already presented two metrization theorems for compact spaces: (1) any compact s … more →
Compact Spaces With G-delta Diagonals
Dan Ma wrote 2 weeks ago: In a previous post, I showed that any compact space with a countable network is metrizable. Another … more →
Network Weight of Topological Spaces - II
Dan Ma wrote 2 weeks ago: This is a continuation of the discussion on network. In the previous post, I showed that the network … more →
Venturing into products and duality
rosskilgore wrote 2 weeks ago: I’m now jumping to Chapter 6 in Bredon, Geometry and Topology. I want to try to get through a … more →
Network Weight of Topological Spaces - I
Dan Ma wrote 2 weeks ago: In the previous post, I discussed the notion of network of a topological space. It was noted that fo … more →
Singular Homology
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Sunny wrote 2 weeks ago: Informally, homology is supposed to characterize the “holes” in a space. Consider a toru … more →
