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Version 1 |
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\begin{defn} \cite{steen, willard}
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\begin{defn} \cite{steen}
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| Suppose $X$ is a topological space. If $X$ has a basis consising of |
Suppose $X$ is a topological space. If $X$ has a basis consising of |
| clopen sets, then $X$ is said to be \PMlinkescapetext{\emph{zero dimensional}}. |
clopen sets, then $X$ is said to be \PMlinkescapetext{\emph{zero dimensional}}. |
| \end{defn} |
\end{defn} |
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| \begin{prop} Every zero dimensional space is $T_3$. |
\begin{prop} Every zero dimensional space is $T_3$. |
| \end{prop} |
\end{prop} |
| \PMlinkname{(proof.)}{EveryZeroDimensionalSpaceIsT_3} |
\PMlinkname{(proof.)}{EveryZeroDimensionalSpaceIsT_3} |
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| \begin{thebibliography}{9} |
\begin{thebibliography}{9} |
| \bibitem{steen} L.A. Steen, J.A.Seebach, Jr., |
\bibitem{steen} L.A. Steen, J.A.Seebach, Jr., |
| \emph{Counterexamples in topology}, |
\emph{Counterexamples in topology}, |
| Holt, Rinehart and Winston, Inc., 1970. |
Holt, Rinehart and Winston, Inc., 1970. |
| \bibitem{willard} S. Willard, \emph{General Topology}, |
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| Addison-Wesley, Publishing Company, 1968. |
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| \end{thebibliography} |
\end{thebibliography} |
