Counterexamples in Topology

Counterexamples in Topology (1970, 2nd ed. 1978) is a book on <a href="/facts/Mathematics/pxTouaz4">mathematics</a> by <a href="/facts/Topology/2EqW47cU">topologists</a> <a href="/facts/Lynn_Steen/JFdvAfpc">Lynn Steen</a> and <a href="/facts/J._Arthur_Seebach,_Jr./sU4TbeUA">J. Arthur Seebach, Jr.</a>
In the process of working on problems like the <a href="/facts/Metrization_problem/BCLdo5Jf">metrization problem</a>, topologists (including Steen and Seebach) have defined a wide variety of <a href="/facts/Topological_properties/vbJR18Sx">topological properties</a>. It is often useful in the study and understanding of abstracts such as <a href="/facts/Topological_space/v2ut7CbK">topological spaces</a> to determine that one property does not follow from another. One of the easiest ways of doing this is to find a <a href="/facts/Counterexample/dnThYpHW">counterexample</a> 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 <a href="/facts/St._Olaf_College/u5C6YxLE">St. Olaf College</a>, <a href="/facts/Minnesota/ncgVuC4Q">Minnesota</a> in the summer of 1967, canvassed the field of <a href="/facts/Topology/2EqW47cU">topology</a> for such counterexamples and compiled them in an attempt to simplify the literature.
For instance, an example of a <a href="/facts/First-countable_space/HDuTYa6A">first-countable space</a> which is not <a href="/facts/Second-countable_space/qw9YdnBN">second-countable</a> is counterexample #3, the <a href="/facts/Discrete_topology/hpvXA23u">discrete topology</a> on an <a href="/facts/Uncountable_set/zl2WqyJQ">uncountable set</a>. 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.

Counterexamples in Topology open-in-new

Counterexamples in Topology