Category: Uncategorized
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Limiting Space of an Edge Replacement System
This is me practicing obtaining limiting spaces of an expanding edge replacement system. While not rigorous (for example, I don’t prove that the limiting space I obtain is homeomorphic to the Vicsek fractral, but it is “obvious”, and I don’t show that the list of equivalent sequences is exhaustive), it is still good for me…
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All metric spaces of finite diameter are quasi-isometric
In this short project we prove that all metric spaces of finite diameter are quasi-isometric. We give the definitions required to understand the problem. The problem itself is easy – this small project is intended to cement my understanding of the material for my more substantial project on geometric group theory.
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An explanation of Commutative Diagrams
Here is a short project I wrote which defines commutative diagrams in terms of directed graphs. I wrote this project because I couldn’t find a good source of information online which explained commutative diagrams to my satisfaction.
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Is (R,+) group isomorphic to (R^2,+)?
The idea to prove this is to show that and are isomorphic as -vector spaces. To do this requires some moving parts, so I’ve compiled them all (except for elementary results from linear algebra and understanding of cardinality) into a single document: