“Fort space”的意思、由来-开放百科全书

词条

Fort space

释义

In mathematics, Fort space, named after M. K. Fort, Jr., is an example in the theory of topological spaces.

Let X be an infinite set of points, of which P is one. Then a Fort space is defined by X together with all subsets A such that:

X is homeomorphic to the one-point compactification of a discrete space.

Modified Fort space is similar but has two particular points P and Q. So a subset is declared "open" if:

Fortissimo space is defined as follows. Let X be an uncountable set of points, of which P is one. A subset A is declared "open" if:

References

M. K. Fort, Jr. "Nested neighborhoods in Hausdorff spaces." American Mathematical Monthly vol.62 (1955) 372.
{{Citation | last1=Steen | first1=Lynn Arthur | author1-link=Lynn Arthur Steen | last2=Seebach | first2=J. Arthur Jr. | author2-link=J. Arthur Seebach, Jr. | title=Counterexamples in Topology | origyear=1978 | publisher=Springer-Verlag | location=Berlin, New York | edition=Dover reprint of 1978 | isbn=978-0-486-68735-3 | mr=507446 | year=1995}}

2 : Topological spaces|Topologies on the set of positive integers

随便看

开放百科全书收录14589846条英语、德语、日语等多语种百科知识，基本涵盖了大多数领域的百科知识，是一部内容自由、开放的电子版国际百科全书。