Topologies of linear continuity
On the real plane the topologiesof linear continuity are introduced, i.e. such topologies continuity of function with respect tothem is equivalent to continuity of all restrictions of this function on the straight line at the plane.Regularity and normality of these topologies are investigated.
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Keywords
product topologies, linear continuity, топологии произведения пространств, линейная непрерывностьAuthors
| Name | Organization | |
| Grinshpon Y.S. | grinshpon@mail.ru |
References
Piotrowski Z., Valin R.W. Separately continuous functions: approximations, extensions, and restrictions // Int. J. Mathematics and Mathematical Sciences. 2003. V. 54. P. 3469 - 3477
Young W.H., Young G.C. Discontinuous functions continuous with respect to every straight line // Quarter Journal of Mathematics. Oxford. 1910. No. 41. P. 87 - 93.
Knight C.J., Moran W., Pym J.S. The topologies of separate continuity. I // Proc. of Cambridge Philosophy Society. 1970. No. 68. P. 663 - 671.
Knight C.J., Moran W., Pym J.S. The topologies of separate continuity. II // Proc. of Cambridge Philosophy Society. 1972. No. 71. P. 307 - 319.
