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Define co-finite topology andco-countable topologyon a set.Among the 2 which isstronger topology?
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part 1,calicut university 2 nd sem msc maths TOPOLOGY module 1 previous year question and answers
COFINITE TOPOLOGY
CO-COUNTABLE TOPOLOGY
Let X be any set and T (topology)consist of ∅ and these A subsets of X such that A'(A compliment ) is countable. such topology is called cocountable topology
If x is not finite then co-finite topology strictly weaker than co-countable topology or if x is finite then Co-countable topology and co-finite topology are equal and same as discrete topology
COFINITE TOPOLOGY
CO-COUNTABLE TOPOLOGY
Let X be any set and T (topology)consist of ∅ and these A subsets of X such that A'(A compliment ) is countable. such topology is called cocountable topology
If x is not finite then co-finite topology strictly weaker than co-countable topology or if x is finite then Co-countable topology and co-finite topology are equal and same as discrete topology
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