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Indiscrete space (Extra: Figure and Calvino)

Here is the begining of Italo Calvino's story All At One Point: For our purposes I have substituted the word 'point' by the phrase 'open set'.

All At One Open Set

Naturally, we were all there, - old Qfwfq said, - where else could we have been. Nobody knew then that there could be space. Or time either: what use did we have for time, packed in there like sardines.

I say "packed like sardines," using a literary image: in reality there wasn't even space to pack us into. Every open set of each of us coincided with every open set of each of the others in a single open set, which was where we all were. In fact, we didn't even bother one another, except for personality differences, because when space doesn't exist, having somebody unpleasant like Mr. Pber^t Pber^d underfoot all the time is the most irritating thing.

Discrete space (Extra Figure)

Cofinite and co-countable topology (Figures 3.1.1 and 3.1.2)

Nested topology (Figures 3.1.3 and 3.1.4)