2 TOPOLOGICAL SPACES
In the previous chapter you studied metric spaces and saw that the definition of a continuous real
valued function of real numbers can be extended to the general setting of metric spaces. In this
chapter we introduce and study topological spaces, which are more general than metric
spaces.
Continuity of functions of topological spaces will then be discussed and we will see that it is a
generalization of continuity of functions on metric spaces.
2.1 Definition and Examples of Topological Spaces
2.2 Bases and Subspace Topologies
2.3 Continuous Functions
2.4 Homeomorphisms
2.5 Product Topologies
2.6 Hausdorff Spaces
2.7 Neighbourhoods, Accumulation Points, Interior Points, Boundary Points
2.8 Practice Problems
2.2 Bases and Subspace Topologies
2.3 Continuous Functions
2.4 Homeomorphisms
2.5 Product Topologies
2.6 Hausdorff Spaces
2.7 Neighbourhoods, Accumulation Points, Interior Points, Boundary Points
2.8 Practice Problems
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