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(Solved): How to solve E_(x_(28)) Let \beta be the collection of Circular regions (interiors of circles) an ...
How to solve
E_(x_(28))Let
\beta be the collection of Circular regions (interiors of circles) and
\beta ^(')be the Collection of rectangular regions (interiors of rectangles) in the plane, with sides para
(%)/()l to
x-axis. (i) Prove that
\beta is a basis for a topology
\tau _(\beta )on the plane. (ii) Prove that
\beta ^(')is a basis for a topology
\tau _(B^('))on the plane. (iii) Prove that
\tau _(B)and
\tau _(B^('))coincide
(\tau _(B))
=(
\tau _(B^('))). # #
E_(E_(xg))Let
Sbe the Collection of all straight lines in the plane which are parallel to the
x-axis. If
Sis a subbasis for a topology
\tau _(on )R^(2), describe all open sets in
(R^(2),\tau ). Ex
x_(3)Answer the same question as in Exas where
Sis now the collection of all circles in the plane. Ex31 Answer the same questionasin
E_(x29)when
Sis the Collection of all circles in the plane which have their centres on the
x-axis.
