- Fort space
A Fort space is an example in the theory of
topological space s.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:
*"A" excludes "P", or
*"A" contains all but a finite number of the points of "X""X" is
homeomorphic to theone-point compactification of adiscrete space .Modified Fort space is similar but has two particular points "P" and "Q". So a subset is declared "open" if:
*"A" excludes "P" and "Q", or
*"A" contains all but a finite number of the points of "X"Fortissimo space is defined as follows. Let "X" be an uncountable set, of which "P" is one. A subset "A" is declared "open" if:
*"A" excludes "P", or
*"A" contains all but a countable set of the points of "X"ee also
*
Arens-Fort space 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 | id=MathSciNet|id=507446 | year=1995
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