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Tag Archives: pathconnected spaces
Topology: Locally Connected and Locally PathConnected Spaces
Locally Connected Spaces Recall that each topological space X is the settheoretic disjoint union of its connected components, but in general (e.g. for X=Q) fails to be the topological disjoint union. The problem is that the connected components in general aren’t open … Continue reading
Topology: PathConnected Spaces
A related notion of connectedness is this: Definition. A path on a topological space X is a continuous map The path is said to connect x and y in X if f(0)=x and f(1)=y. X is said to be pathconnected if any two points … Continue reading
Posted in Notes
Tagged advanced, connected components, connected spaces, pathconnected components, pathconnected spaces, topology
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