Learning by Glueing

I wish to express my gratitude to many authors.
Thanks to Martin Gardner, whose puzzles, contributed by many authors, still fascinate me.
Thanks to D.R. Hofstadter who continued his column.
Thanks to godfather Gauss, who regarded the infinite as façon de parler.
Thanks to Conway, who finally demonstrated that even the most surreal numbers are just finite  games.
Thanks to Doron Zeilberger, whose opinions convinced me to abandon all this ε – δ – nonsense.
Thanks to Roger Penrose. The Emperor’s new Mind is a book full of fascinating physics. It does not leave much to do for mere mortals, though.

I renounce platonism. I do not believe this obscurantist drivel any more!

All topological spaces considered here are finite. Monsters and AC need not apply. The topology is just combinatorics in disguise. Moreover, the spaces are finite in a very concrete, realistic sense: They are address spaces of bulk digital memory, glued and twisted in a lexer-like manner, constantly ripped apart and re-glued again. The set of all A is some kind of geometric object in these finite spaces, although its construction will not be finished as long as there are minds using it.

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