| Friday 26 April 2024 | |
| Events for day: Wednesday 18 April 2018 |
| 15:30 - 17:00 Geometry and Topology Weekly Seminar Connectifying a Topological Space by Adding one Point School MATHEMATICS In 1924, P. Alexandroff proved that a locally compact $T_2$-space has a $T_2$ one-point compactification (obtained by adding a ``point at infinity'') if and only if it is non-compact. He also asked for characterizations of spaces which have one-point connectifications. Here, we consider one-point connectifications, and in analogy with Alexandroff's theorem, we show that in the realm of $T_i$-spaces ($i=3frac{1}{2},4,5$) a locally connected space has a one-point connectification if and only if it has no compact component. We explain how this theorem may be extended to the case $i=2$ and to the case $i=6$ under the set-theoretic assumption $m ... |