ONT Re: Topology
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| 1. Topological Spaces
|
| 1.5. Interior and Boundary (cont.)
|
| If X is an indiscrete space the interior of every set except X itself
| is void. If X is a discrete space, then each set is open and closed
| and consequently identical with its interior and with its closure.
| If X is the set of real numbers with the usual topology, then the
| interior of the set of all integers is void; the interior of a
| closed interval is the open interval with the same endpoints.
| The interior of the set of rational numbers is void, and the
| closure of the interior of this set is consequently void.
| The closure of the set of rational numbers is the set X
| of all numbers, and the interior of this set is X again.
| Thus the interior of the closure of a set may be quite
| different from the closure of the interior; that is,
| the interior operator and the closure operator do not
| generally commute.
|
| JLK, Gen Top, page 45.
|
| John L. Kelley, 'General Topology',
| Van Nostrand Reinhold, New York, NY, 1955.
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