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What is Topology? Undergraduate studies Graduate studies Employment opportunities Visitor directions. General Topology or Point Set Topology. General topology normally considers local properties of spaces, and is closely related to analysis.

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It generalizes the concept of continuity to define topological spaces, in which limits of sequences can be considered. Sometimes distances can be defined in these spaces, in which case they are called metric spaces; sometimes no concept of distance makes sense.


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  • Combinatorial Topology. Combinatorial topology considers the global properties of spaces, built up from a network of vertices, edges, and faces. This is the oldest branch of topology, and dates back to Euler.

    Strange topological materials are popping up everywhere physicists look

    It has been shown that topologically equivalent spaces have the same numerical invariant, which we now call the Euler characteristic. Algebraic Topology. Algebraic topology also considers the global properties of spaces, and uses algebraic objects such as groups and rings to answer topological questions. Lodging information.

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    Understanding Topology Provides an overview of how to define cluster topology. MapR 6.

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