#topology — Public Fediverse posts

While teaching a course on algebraic theories last semester I mentioned at some point that the familiar bicomplete categories Top and Poset were not algebraic, but were topological. A student asked about this later on and I found that the #Wikipedia page on «topological category» pointed to categories enriched in Top, not categories with a forgetful functor to Set which is topological. While I have lost a lot of faith in Wikipedia recently, I am pleased to report that https://en.wikipedia.org/wiki/Topological_category is now a disambiguation page.

#math #mathematics #topology #algebra #CategoryTheory

💁🏻‍♀️ TIL: 🧵🌐 The hairy ball #theorem says you can’t comb a #sphere smooth without a cowlick somewhere.

The same rule explains why #Earth always has a #cyclone spinning, why #fusion reactors use #doughnut shapes, and why omnidirectional antennas can’t exist. #Wind patterns over the #Arctic and #Antarctic circles illustrate the proof.

👉 https://www.scientificamerican.com/article/how-maths-hairy-ball-theorem-could-explain-bad-hair-days/

#topology #math #weather #hurricane #nuclearfusion #tokamak #plasma #science #hair

Black holes and topological vortices in a discrete spacetime lattice.
This is not an animation.

I created a simulation where particle stability is maintained by internal field tension rather than hard coded rules. I didn't program any velocity increase the geometry itself is generating the motion.

#Topology
#Gravity
#blackholes
#nonlineardynamics
#Superfluid #Physics
#Simulation
#QuantumPhysics
#computationalphysics
#emergence

Black holes and topological vortices in a discrete spacetime lattice.
This is not an animation.

#Topology
#Gravity
#blackholes
#nonlineardynamics
#Superfluid #Physics
#Simulation
#QuantumPhysics
#computationalphysics
#Emergence

River Network Routing And Discharge Partitioning On A Multichannel River Network
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https://doi.org/10.1029/2025WR041417 <-- shared paper
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"... KEY POINTS:
• River multifurcation pathways were identified in a vector river network globally
• A multifurcation scheme was added to a river network routing model to split river discharge at divergences
• Accounting for multichannels improved discharge accuracy and resulted in earlier arrival of flood waves downstream of divergences…”
#GIS #spatial #mapping #spatialanalysis #spatiotemporal #model #modeling #water #hydrology #river #stream #watercourse #floods #flooding #risk #hazard #benefit #network #segment #downstream #upstream #braiding #sinuosity #delta #complexity #flowdirection #remotesensing #confluence #bifurcations #divergence #multifurcation #discharge #topology #routing #global #landsurface #Pfafstetter #basin

The name for the algebraic structure consisting of a set \(A\) equipped with a binary operation \(f\colon A^2\to A\) which is not assumed to be commutative, associative, etc. has an interesting history. As far as I can tell, this sort of algebra was originally known as a "groupoid", and you can find recent literature using the term in that way. However, Nicolas Bourbaki called a set with a single binary operation a "magma" in his Éléments de mathématique and this name came to be used when there might be confusion with the newer topological use of "groupoid" to mean a category whose morphisms are all invertible. A third contender is "binar". I don't know the history of this one but it seems reasonable to me.

I prefer "magma" myself. I don't know what a "lava" or a "volcano" should be nor have I had the audacity to try to name something like this in the literature. One reason I prefer "magma" is that I can talk about a set \(A\) equipped with a single \(n\)-ary operation \(f\colon A^n\to A\) as an "\(n\)-ary magma" (or just "\(n\)-magma" or even "magma").

#algebra #UniversalAlgebra #topology #bourbaki #terminology