Analysis - Cardinality of the Continuum: Collection of all open (closed or perfect) subsets of R

Описание к видео Analysis - Cardinality of the Continuum: Collection of all open (closed or perfect) subsets of R

Let c denote the cardinality of the Continuum.
Let F be a closed subset of R and let G be an open subset of R. Show that F is an intersection of countably many open sets and G is a union of countably many closed sets.
Let D be the collection of all open subsets of R. Show that the cardinality of D is c.
Let F be the collection of all closed subsets of R. Show that the cardinality of F is c.
A subset of a topological space X is perfect if A = A'. Let P be the collection of all perfect sets in R. Show that the cardinality of P is c.

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