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Lesson Posted on 26/09/2018 Learn Mathematics
Shruti
Regular Spaces:The properties of topological spaces are in general quite different from those of metric spaces, so some additional restrictions are often imposed on a topology in order to bring the properties of the corresponding
space closer to those of metric spaces.
Definition: A space X is T3 if for each point x ∈ X and each closed set F ⊆ X with x /∈ F, there are disjoint open sets U and V such that x ∈ U and F ⊆ V . The space X is called regular if it satisfies both T1 and T3 axioms.
Normal Spaces: Topological spaces satisfying this condition are quite close to metric spaces; in fact, it gives a characterisation of second countable metric spaces. We will also see that a continuous function defined on a closed subspace of a topological space with this property admits a continuous extension to the whole space.
Definition: A space X is T4 if each pair of disjoint closed subsets of X have disjoint nbds. X is normal if it satisfies both the T1 and T4 axioms.
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Rachna Sharma
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Shubham Singla
Mathematics is life
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First disadvantages
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Now advantage
It always increase ur knowledge
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Answered on 21/08/2018 Learn Mathematics
Sachin Sheoran
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Ruby S.
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Abhyaas Coaching Centre Indirapuram
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I hv chemistry teacher qualified CSIR -UGC-NET & GATE with all India rank -6 with 5 years tec exp...
Answered on 09/07/2018 Learn Mathematics
Dr. Pratibha Bhawar
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Answered on 21/08/2018 Learn Mathematics
Dhaarini Academy of Technical Education
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Answered on 29/06/2018 Learn Mathematics
Margus Learning
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Time is more important which we have to give our parents, children and sibiling.
As far as all these things are concern start the coaching business.
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Take the coaching from 9- msc.
Margus Institute Gurugram
Krishna Sir
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