Chapter: Continuity
Functions on topological spaces help to study their properties and to construct new spaces from previously existing ones. The most important type of functions in topology are continuous functions. Not surprisingly, they can be defined for general topological spaces, without making use of a whatsoever "distance" concept. This chapter demonstrates how. Also, the important concept of homeomorphism is introduced.
Table of Contents
Examples: 1
 Definition: Continuous Function
 Proposition: Equivalent Notions of Continuous Functions
 Proposition: Continuity of Compositions of Functions
 Definition: Open and Closed Functions
 Proposition: Bijective Open Functions
 Definition: Homeomorphism, Homeomorphic Spaces
 Proposition: Equivalent Notions of Homeomorphisms
 Definition: Topological, Continuous, Open, and Closed Invariants
Mentioned in:
Parts: 1
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References
Bibliography
 Steen, L.A.;Seebach J.A.Jr.: "Counterexamples in Topology", Dover Publications, Inc, 1970
 Jänich, Klaus: "Topologie", Springer, 2001, 7th Edition