Topic: The Subspace Topology

When Ambient Openness Passes to a Subspace

Topologies on Real Intervals

The Topology Induced on a Subset

The Circle’s Relative Topology in the Plane

Restricting a Continuous Map to a Subspace

Relative Neighborhoods and Local Tests

Open Sets Relative to an Ambient Space

Open Caps and Neighborhoods on the Sphere

Nested Subspaces and Transitivity

Inclusion Maps as Continuous Maps