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The Sierpinski space is a particular [[topological space]].  It consists of the set $\{a,b\}$ with open sets $\{ \emptyset, \{a\}, \{a,b\} \}$.  

====References====
* Steen, Lynn Arthur; Seebach, J.Arthur jun. ''Counterexamples in topology'' (2nd ed.) Springer (1978) {{ZBL|0386.54001}}

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Sierpinski space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Sierpinski_space&oldid=37239

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