Editing Counterexamples in Topology (section)

{{short description|Book by Lynn Steen}}
{{Infobox book 
| name          = Counterexamples in Topology
| image         = Counterexamples in Topology.jpg
| caption       = 
| author        = [[Lynn Steen|Lynn Arthur Steen]]<br>[[J. Arthur Seebach, Jr.]]
| country       = United States
| language      = English
| series        = 
| genre         = Non-fiction
| subject       = [[Topological space]]s
| publisher     = [[Springer-Verlag]]
| release_date  = 1970
| media_type    = [[Hardback]], [[Paperback]]
| pages         = 244 pp.
| isbn =  0-486-68735-X
| dewey= 514/.3 20
| congress= QA611.3 .S74 1995
| oclc= 32311847
}}

'''''Counterexamples in Topology''''' (1970, 2nd ed. 1978) is a book on [[mathematics]] by [[topology|topologist]]s [[Lynn Steen]] and [[J. Arthur Seebach, Jr.]]

In the process of working on problems like the [[metrization problem]], topologists (including Steen and Seebach) have defined a wide variety of [[topological properties]].  It is often useful in the study and understanding of abstracts such as [[topological space]]s to determine that one property does not follow from another.  One of the easiest ways of doing this is to find a [[counterexample]] which exhibits one property but not the other.  In ''Counterexamples in Topology'', Steen and Seebach, together with five students in an undergraduate research project at [[St. Olaf College]], [[Minnesota]] in the summer of 1967, canvassed the field of [[topology]] for such counterexamples and compiled them in an attempt to simplify the literature.

For instance, an example of a [[first-countable space]] which is not [[second-countable space|second-countable]] is counterexample #3, the [[discrete topology]] on an [[uncountable set]].  This particular counterexample shows that second-countability does not follow from first-countability.

Several other "Counterexamples in ..." books and papers have followed, with similar motivations.