Show that the collection of radially open sets is a topology for R^2.
A subset of R2 is called...

Question

Show that the collection of radially open sets is a topology for R^2.
A subset of R2 is called radially open if it contains open line segment in each direction about each of its points.

David · Accepted Answer

Collection τ on R2, such that U ∈ τ if for every x ∈ U , line segment in each
direction around x contained in U .
For understanding U , Let describe point on U an line segments. Give polar
coordinate(r, θ) system on R2, we choose the coordinate such that x become
poles.

Show that the collection of radially open sets is a topology for R^2. A subset of R 2 is called radially open if it contains open line segment in each direction about each of its points.

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