The downtown area of Logic City is a Manhattan-like grid, with “streets” running East-West and “avenues” North-South. Each block is two units long in the East-West direction and one unit in the North-South direction, like in the image above.¹

We say that the locations X and Y (for instance) are “at diagonally opposite corners of the same block”, and that Z is due South of Y and due South-West of X. Note that “due South-West” means strictly on the 45^o line, not just somewhere in the South-West quadrant.

There are 8 streets (First Street, …, Eighth Street) and likewise 6 avenues. First Street is the Northern edge of the downtown area, and First Avenue is its Western edge.

On certain of the corners are six of the most famous city landmarks. The Hauptsatz Monument is due SE from Cantor’s Paradise and two blocks N of Hilbert’s Hotel. If you walk three blocks North from the Hauptsatz and then turn and walk two blocks East, you arrive at the Domain. If you then again walk North, you eventually arrive at a point due East of Cantor’s. The Domain and the Co-domain are at diagonally opposite corners of a block, the Co-domain being due NE of Hilbert’s and S of the Homomorphic Image.

Give the addresses (street and avenue) of the six landmarks.

¹   For the purposes of geometry, streets and avenues are just lines which intersect at points. In real life, as in the diagram, roads have width greater than zero, but we ignore this for reasoning purposes.