Rigid graphs of maps
Abstract
In this note 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×Y. From this result it follows that there is no maximal topology among metric separable connected topologies on a given set X.
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2. J. de Groot, Groups represented by homeomorphism groups I, Math. Ann. 138 (1959), 80-102.
3. F.B. Jones, Connected and disconnected plane sets and the functional equation f(x)+f(y) = f(x+y), Bull. Amer. Math. Soc. 48 (1942), 115-120.
4. W. Kulpa, On the existence of maps having graphs connected and dense, Fund. Math. 76 (1972), 207-211.
5. W. Sierpiński, Sur les types d'ordre des ensembles lineaires, Fund. Math. 37 (1950), 253-264.
KulpaW. (1986). Rigid graphs of maps. Annales Mathematicae Silesianae, 2, 92-95. Retrieved from https://www.journals.us.edu.pl/index.php/AMSIL/article/view/14328
Władysław Kulpa
Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
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