real analysis with point set topology

Table of Contents:
1 Sets and Functions
1.1 Sets
1.2 Functions
1.3 Finite and Infinite Sets
2 The Real Numbers
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Table of Contents:
1 Sets and Functions
1.1 Sets
1.2 Functions
1.3 Finite and Infinite Sets
2 The Real Numbers
2.1 Properties of Real Numbers
2.2 Construction of the Real Numbers
3 Topology
3.1 Topological Spaces
3.2 Open Sets and Closed Sets
4 Continuous Functions
4.1 Continuity
4.2 Connectedness and Compactness
5 Sequences and Series
5.1 Sequences
5.2 Real Sequences
5.3 Infinite Series
5.4 Functional Limits
6 Metric Spaces
6.1 The Metric Topology
6.2 Continuity in Metric Spaces
6.3 Sequences in Metric Spaces
6.4 Completion of Metric Spaces
7 Sequences of Functions
7.1 Pointwise and Uniform Convergence
7.2 Function Spaces and Uniform Approximation
8 Calculus
8.1 The Riemann Integral
8.2 Properties of the Integral
8.3 The Derivative
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