ON COUNTABLE CONNECTED HAUSDORFF SPACES IN WHICH THE INTERSECTION OF EVERY PAIR OF CONNECTED SUBSETS IS CONNECTED

V. TZANNES

《International Journal of Mathematics and Mathematical Sciences》 1998卷 (1998/12) Pp. 459-462

https://doi.org/10.1155/S0161171298000635

摘要

We prove that a countable connected Hausdorff space in which the intersection of every pair of connected subsets is connected, cannot be locally connected, and also that every continuous function from a countable connected, locally connected Hausdorff space, to a countable connected Hausdorff space in which the intersection of every pair of connected subsets is connected, is constant.

關鍵字

Countable connected ； locally connected