MATHMJ05: Theory of Real Functions & Metric | Semester IV | Vidyasagar University

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MATHMJ05: Theory of Real Functions & Metric Curriculum Map

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Concepts

ApexMath Curriculum Mapatlas
Metric Axioms and Subspace Metricssubsection
University: Vidyasagar University / B.Sc. 4 Years Honours in Mathematics under NEP / Semester IV / MATHMJ05: Theory of Real Functions & Metriccurriculum
Standard Metrics on Euclidean Spacessubsection
Bounded Metrics from Existing Metricssubsection
Pseudometrics and Quotient Metricssubsection
Metrics on Extended Spacessubsection
Metrics on Sequence Spacessubsection
Metrics on Function Spacessubsection
Limits of Sequences in Metric Spacessubsection
Subsequences and Cauchy Criteriasubsection
Cauchy Sequences in Metric Spacessubsection
Complete and Incomplete Metric Spacessubsection
Completeness of Standard Metric Spacessubsection
Coordinatewise and Uniform Convergencesubsection
Complete Function Spaces and Sequence Problemssubsection
Completion and Isometric Embeddingsubsection
Constructed Metrics and Practice Problemssubsection
Metric Balls and Neighbourhoodssubsection
Open Sets and Interiorsubsection
Closed Sets and Complementationsubsection
Limit Points and Closuresubsection
Boundary and Exterior of Setssubsection
Bounded Sets and Diameterssubsection
Relative Topology of Subspacessubsection
Completeness of Subspacessubsection
Nested Closed Sets in Complete Spacessubsection
Separable Metric Spacessubsection
Countability Bases in Metric Spacessubsection
Lindelof and Dense Metric Spacessubsection
Category and Nowhere Dense Setssubsection
Baire Category Theorem and Applicationssubsection
Oscillation and Sets of Discontinuitysubsection

Relationships

ApexMath Curriculum Map --contains--> University: Vidyasagar University / B.Sc. 4 Years Honours in Mathematics under NEP / Semester IV / MATHMJ05: Theory of Real Functions & Metric
University: Vidyasagar University / B.Sc. 4 Years Honours in Mathematics under NEP / Semester IV / MATHMJ05: Theory of Real Functions & Metric --maps-to--> Metric Axioms and Subspace Metrics
University: Vidyasagar University / B.Sc. 4 Years Honours in Mathematics under NEP / Semester IV / MATHMJ05: Theory of Real Functions & Metric --maps-to--> Standard Metrics on Euclidean Spaces
University: Vidyasagar University / B.Sc. 4 Years Honours in Mathematics under NEP / Semester IV / MATHMJ05: Theory of Real Functions & Metric --maps-to--> Bounded Metrics from Existing Metrics
University: Vidyasagar University / B.Sc. 4 Years Honours in Mathematics under NEP / Semester IV / MATHMJ05: Theory of Real Functions & Metric --maps-to--> Pseudometrics and Quotient Metrics
University: Vidyasagar University / B.Sc. 4 Years Honours in Mathematics under NEP / Semester IV / MATHMJ05: Theory of Real Functions & Metric --maps-to--> Metrics on Extended Spaces
University: Vidyasagar University / B.Sc. 4 Years Honours in Mathematics under NEP / Semester IV / MATHMJ05: Theory of Real Functions & Metric --maps-to--> Metrics on Sequence Spaces
University: Vidyasagar University / B.Sc. 4 Years Honours in Mathematics under NEP / Semester IV / MATHMJ05: Theory of Real Functions & Metric --maps-to--> Metrics on Function Spaces
University: Vidyasagar University / B.Sc. 4 Years Honours in Mathematics under NEP / Semester IV / MATHMJ05: Theory of Real Functions & Metric --maps-to--> Limits of Sequences in Metric Spaces
University: Vidyasagar University / B.Sc. 4 Years Honours in Mathematics under NEP / Semester IV / MATHMJ05: Theory of Real Functions & Metric --maps-to--> Subsequences and Cauchy Criteria
University: Vidyasagar University / B.Sc. 4 Years Honours in Mathematics under NEP / Semester IV / MATHMJ05: Theory of Real Functions & Metric --maps-to--> Cauchy Sequences in Metric Spaces
University: Vidyasagar University / B.Sc. 4 Years Honours in Mathematics under NEP / Semester IV / MATHMJ05: Theory of Real Functions & Metric --maps-to--> Complete and Incomplete Metric Spaces
University: Vidyasagar University / B.Sc. 4 Years Honours in Mathematics under NEP / Semester IV / MATHMJ05: Theory of Real Functions & Metric --maps-to--> Completeness of Standard Metric Spaces
University: Vidyasagar University / B.Sc. 4 Years Honours in Mathematics under NEP / Semester IV / MATHMJ05: Theory of Real Functions & Metric --maps-to--> Coordinatewise and Uniform Convergence
University: Vidyasagar University / B.Sc. 4 Years Honours in Mathematics under NEP / Semester IV / MATHMJ05: Theory of Real Functions & Metric --maps-to--> Complete Function Spaces and Sequence Problems
University: Vidyasagar University / B.Sc. 4 Years Honours in Mathematics under NEP / Semester IV / MATHMJ05: Theory of Real Functions & Metric --maps-to--> Completion and Isometric Embedding
University: Vidyasagar University / B.Sc. 4 Years Honours in Mathematics under NEP / Semester IV / MATHMJ05: Theory of Real Functions & Metric --maps-to--> Constructed Metrics and Practice Problems
University: Vidyasagar University / B.Sc. 4 Years Honours in Mathematics under NEP / Semester IV / MATHMJ05: Theory of Real Functions & Metric --maps-to--> Metric Balls and Neighbourhoods
University: Vidyasagar University / B.Sc. 4 Years Honours in Mathematics under NEP / Semester IV / MATHMJ05: Theory of Real Functions & Metric --maps-to--> Open Sets and Interior
University: Vidyasagar University / B.Sc. 4 Years Honours in Mathematics under NEP / Semester IV / MATHMJ05: Theory of Real Functions & Metric --maps-to--> Closed Sets and Complementation
University: Vidyasagar University / B.Sc. 4 Years Honours in Mathematics under NEP / Semester IV / MATHMJ05: Theory of Real Functions & Metric --maps-to--> Limit Points and Closure
University: Vidyasagar University / B.Sc. 4 Years Honours in Mathematics under NEP / Semester IV / MATHMJ05: Theory of Real Functions & Metric --maps-to--> Boundary and Exterior of Sets
University: Vidyasagar University / B.Sc. 4 Years Honours in Mathematics under NEP / Semester IV / MATHMJ05: Theory of Real Functions & Metric --maps-to--> Bounded Sets and Diameters
University: Vidyasagar University / B.Sc. 4 Years Honours in Mathematics under NEP / Semester IV / MATHMJ05: Theory of Real Functions & Metric --maps-to--> Relative Topology of Subspaces
University: Vidyasagar University / B.Sc. 4 Years Honours in Mathematics under NEP / Semester IV / MATHMJ05: Theory of Real Functions & Metric --maps-to--> Completeness of Subspaces
University: Vidyasagar University / B.Sc. 4 Years Honours in Mathematics under NEP / Semester IV / MATHMJ05: Theory of Real Functions & Metric --maps-to--> Nested Closed Sets in Complete Spaces
University: Vidyasagar University / B.Sc. 4 Years Honours in Mathematics under NEP / Semester IV / MATHMJ05: Theory of Real Functions & Metric --maps-to--> Separable Metric Spaces
University: Vidyasagar University / B.Sc. 4 Years Honours in Mathematics under NEP / Semester IV / MATHMJ05: Theory of Real Functions & Metric --maps-to--> Countability Bases in Metric Spaces
University: Vidyasagar University / B.Sc. 4 Years Honours in Mathematics under NEP / Semester IV / MATHMJ05: Theory of Real Functions & Metric --maps-to--> Lindelof and Dense Metric Spaces
University: Vidyasagar University / B.Sc. 4 Years Honours in Mathematics under NEP / Semester IV / MATHMJ05: Theory of Real Functions & Metric --maps-to--> Category and Nowhere Dense Sets
University: Vidyasagar University / B.Sc. 4 Years Honours in Mathematics under NEP / Semester IV / MATHMJ05: Theory of Real Functions & Metric --maps-to--> Baire Category Theorem and Applications
University: Vidyasagar University / B.Sc. 4 Years Honours in Mathematics under NEP / Semester IV / MATHMJ05: Theory of Real Functions & Metric --maps-to--> Oscillation and Sets of Discontinuity

Concepts

Relationships

Mapped learning units

Introduction to Metric Spaces

Metric Axioms and Subspace Metrics

Standard Metrics on Euclidean Spaces

Bounded Metrics from Existing Metrics

Pseudometrics and Quotient Metrics

Metrics on Extended Spaces

Metrics on Sequence Spaces

Metrics on Function Spaces

Limits of Sequences in Metric Spaces

Subsequences and Cauchy Criteria

Cauchy Sequences in Metric Spaces

Complete and Incomplete Metric Spaces

Completeness of Standard Metric Spaces

Coordinatewise and Uniform Convergence

Complete Function Spaces and Sequence Problems

Completion and Isometric Embedding

Constructed Metrics and Practice Problems

Topological Structure of Metric Spaces

Metric Balls and Neighbourhoods

Curated pathways

Metric Spaces

Open Sets and Interior

Closed Sets and Complementation

Limit Points and Closure

Boundary and Exterior of Sets

Bounded Sets and Diameters

Relative Topology of Subspaces

Completeness of Subspaces

Nested Closed Sets in Complete Spaces

Separable Metric Spaces

Countability Bases in Metric Spaces

Lindelof and Dense Metric Spaces

Category and Nowhere Dense Sets

Baire Category Theorem and Applications

Oscillation and Sets of Discontinuity

Introduction To Discrete Mathematics