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PDF-Chapter5CountabilityandSeparationAxioms5.1FirstandSecondCountableTopol

PDF-Chapter5CountabilityandSeparationAxioms5.1FirstandSecondCountableTopol

Author : danika-pritchard | Published Date : 2016-09-28

nn2NgisacountablelocalbasisatxHenceXJdisa rstcountablespaceSowesaythateverymetricspaceXdisa rstcountablespaceiiLetXNandJfXf1gf12gf12nggthenobviouslyXJisa rstcou

n):n2Ngisacountablelocalbasisatx.Hence(X Jd)isa rstcountablespace.So wesaythateverymetricspace(X;d)isa rstcountablespace.(ii)LetX=NandJ=f;X;f1g;f1;2g;:::;f1;2;:::;ng;:::;gthenobviously(X;J)isa rstcou

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