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\def\u{\underbar}

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\ctln{\bf Math 970 Homework \# 6}

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\ctln{{\bf Due: } Oct. 16}

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\item{27.} Show that if ${\Cal T}\subseteq {\Cal T}^\prime$ are topologies on
$X$ and $(X,{\Cal T}^\prime)$ is connected, then so is $(X,{\Cal T})$.

\bsk

\item{28.} Find an example of a space $X$ and subset $A\subseteq X$ where 
int$(A)$ and cl$(A)$ are both connected, but $A$ is not.

\bsk

\item{29.} Show by example that for $f : X \rightarrow Y$ continuous and $A\subseteq Y$, 
having one of  $f^{-1}(A)$ and $A$  connected does \underbar{not} necessarily imply that the 
other is connected.


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