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Latest Metric Spaces Notes
The Lipshitz Condition
Proof that the Smallest Closed Set Containing a Set is the Closure of the Set
Proof that the Limit of a Uniformly Convergent Sequence of Bounded Mappings is Bounded
Proof that Intersection and Union of Closed Spaces are Closed
Proof that Every Subset of a Set is Contained in its Closure and is Closed iff it is Contained in its Closure
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Metric Spaces
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Normed Linear Spaces
Open Balls in a Metric Space
Open Sets and Continuity in a Metric Space
Possible Metrics
Proof That a Convergent Sequence in a Metric Space Has a Unique Limit
Proof That Any Intersection of Open Balls Contains an Open Ball
Proof that Closed Disjoint Subsets of a Metric Space are Contained in Open Disjoint Subsets
Proof that Every Subset of a Set is Contained in its Closure and is Closed iff it is Contained in its Closure
Proof that Intersection and Union of Closed Spaces are Closed
Proof that the Limit of a Uniformly Convergent Sequence of Bounded Mappings is Bounded
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