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Rigid graphs of maps. (English) Zbl 0593.54013

Pr. Nauk Uniw. Śląsk. Katowicach 752, Ann. Math. Silesianae 2(14), 92-95 (1986).
Summary: We construct maps between metric separable connected spaces X and Y such that the graphs are connected, dense and rigid subspaces of the Cartesian product \(X\times Y\). From this result it follows that there is no maximal topology among metric separable connected topologies on a given set X.

MSC:

54C10 Special maps on topological spaces (open, closed, perfect, etc.)
54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)