2006-28.md

course	course_year	question_number	tags	title	year
Metric and Topological Spaces	IB	28	IB 2006 Metric and Topological Spaces	3.I.4F	2006

Which of the following are topological spaces? Justify your answers.

(i) The set $X=\mathbf{Z}$ of the integers, with a subset $A$ of $X$ called "open" when $A$ is either finite or the whole set $X$;

(ii) The set $X=\mathbf{Z}$ of the integers, with a subset $A$ of $X$ called "open" when, for each element $x \in A$ and every even integer $n, x+n$ is also in $A$