Topology module 1
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1
Define co-finite topology andco-countable topologyon a set.Among the 2 which isstronger topology?
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2
define base for a topology.an example for a base for the usual topology on the set of real numbers
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3
prove that intersection of 2 open sets in a metric space is open
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4
determine the topology induced by discrete metric on a set
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5
if a space is second countable then prove that every open cover of it has a countable subcover
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6
Prove that if the space (X, T) has a base of cardinality α,then cardinality of T cannot exceed 2^α
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7
PT usual topology on the euclidean plane R² is strictly weaker than lexicographic order topology
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8
write the discrete topology on the set s={1,2,3}
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9
define co-countable topology.is it a Hausdorff topology?
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10
prove that second countability is a hereditary property
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11
prove that Union of two closed sets in a metric space is closed
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12
example of an open set,which is not an open interval in the set of real numbers with usual topology
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13
prove that composition of two continuous functions is continuous
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