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Differential Geometry | Topology
Prove that a subspace of a real line with the usual topology is connected if and only if it is an interval
Differential Geometry | Topology
Prove that a countable product of connected space is connected
Differential Geometry | Topology
Prove that any set with the cofinite topology is compact
Differential Geometry | Topology
Prove that any collection of subsets of a set X is a sub base for some topology on X
Differential Geometry | Topology
Give an example of a projection. Which is not closed
Differential Geometry | Topology
Prove that the real line is a homeomorphic to the interval (0,1) with the subspace topology
Differential Geometry | Topology
Give an example of a nowhere dense set in a metric space .substantiate your claim
Differential Geometry | Topology
Prove or disaprove .The intersection of two dense subsets of a metric space is also dense in it
Differential Geometry | Topology
Give examples of two metrics on R ^2 which are not equivalent .substantiate your claim
Differential Geometry | Topology
Given a metric d on a set X prove that there exists an equivalent bounded metric d' on X
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#339914 on Dec 2023
#339914 on Dec 2023