%The Exam.tex environment consists of three files, this one 
%(ExamTemplate.tex), 
%ExamQuestions.tex, and
%DoPlainExam.tex. ExamTemplate.tex is the
%file which you run through TeX. It calls the other files,
%ExamQuestions.tex and DoPlainExam.tex. The actual problems
%for the exam are contained in ExamQuestions.tex, in the order
%in which they are to appear on the actual exam. See the header
%at the beginning of ExamQuestions.tex to see how one types in
%the exam problems. The file DoPlainExam.tex contains the 
%definitions of all the command sequences used. It should not need to
%be modified. One will want to modify the various parameters
%found below in this file, ExamTemplate.tex, such as the coursename,
%the name of the exam, date and instructions, to correspond to 
%the particulars of the current exam. 

%Two notes: 
%[1] You may substitute any name you wish for the file
%ExamQuestions.tex, but it must end in .tex and it should have no
%spaces in it. For example, call it Exam1quests.tex, but in this case
%you must change the line \def\questionsfile{ExamQuestions} which
%you'll see below to: \def\questionsfile{Exam1quests}.
%[2] If you wish the exam to have a grade panel on the first page
%(i.e., a place where one can enter the scores awarded for each
%problem and the total), set the \gradegridflag to 1 below;
%otherwise set it to 0.



\magnification=1200
\hsize=5.4in
\vsize=8in
\def\coursename{Math 471/871}
\def\NameOfExam{Exam I}
\def\examdate{March~4,~1992}
\def\instructions{\vbox{\noindent{\it Instructions\/}: 
Do any three of the following problems.
Note that, when giving a counterexample, you do not need to give a complete
justification, but do point out why your counterexample works. 
For example, to show that not every product of discrete 
spaces is discrete, it would suffice to mention that,
if $X$ is an infinite set and $Y$ is a discrete space having at least
two elements, then $Y^X$ is not discrete, since, 
for any nonempty open subset $U$ of $Y^X$,
$\pi_x(U)=Y$ for infinitely many $x\in X$. \numberofpages}}

\def\gradegridflag{1}
\def\questionsfile{ExamQuestions}

\def\examheader{\hbox to\hsize{\hss}\vskip -.5in
\hbox to\hsize{\hrulefill}
\line{\bf \examdate \hfill \coursename \hfill \NameOfExam}\vskip -.1in
\hbox to\hsize{\hrulefill}
\vskip .1in
\line{\hfill NAME:\hbox to 3in{\hrulefill}}
\vskip .1in
\instructions 
\hbox to\hsize{\hrulefill}}

\input DoPlainExam