Metric and Topological Spaces

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Author(s): J. Rasmussen, ed. Dexter Chua
Series: Cambridge Mathematical Tripos Part IB Lecture Notes
Publisher: University of Cambridge
Year: 2015

Language: English
City: Cambridge
Tags: maths; mathematics; math; advanced; college; university; higher; further; pure; applied; topology

Introduction
Metric spaces
Definitions
Examples of metric spaces
Norms
Open and closed subsets
Topological spaces
Definitions
Sequences
Closed sets
Closure and interior
Closure
Interior
New topologies from old
Subspace topology
Product topology
Quotient topology
Connectivity
Connectivity
Path connectivity
Higher connectivity*
Components
Path components
Connected components
Compactness
Compactness
Products and quotients
Products
Quotients
Sequential compactness
Completeness