Lecture 53 | X is connected iff the only empty set and X itself are closed and open | Topology

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Lecture 52 | X is connected iff the only empty set and X itself are closed and open | Topology Lecture 52 | X is connected iff the only empty set and X itself are closed and open | Topology
THEOREM 2 | IF Y IS CONNECTED IFF. THE ONLY SUBSET THAT ARE OPEN & CLOSED IN X ARE EMPTY & X ITSELF THEOREM 2 | IF Y IS CONNECTED IFF. THE ONLY SUBSET THAT ARE OPEN & CLOSED IN X ARE EMPTY & X ITSELF
DEFINITION FOR CONNECTED | THE ONLY SUBSET ARE BOTH OPEN & CLOSED IN X ARE EMPTY SET & X ITSELF DEFINITION FOR CONNECTED | THE ONLY SUBSET ARE BOTH OPEN & CLOSED IN X ARE EMPTY SET & X ITSELF
Open, closed, clopen sets Open, closed, clopen sets
topological space is disconnected iff X contains a non empty subset A which is both open and closed topological space is disconnected iff X contains a non empty subset A which is both open and closed
Functional Analysis 3 | Open and Closed Sets Functional Analysis 3 | Open and Closed Sets
The topological space X is connected Iff the only subset of X which Is open and closed Is X itself. The topological space X is connected Iff the only subset of X which Is open and closed Is X itself.
A topological space is connected iff the only subset of X which is both open and closed X itself A topological space is connected iff the only subset of X which is both open and closed X itself