Characterizing continuity by preserving compactness and connectedness
| dc.creator | Gerlits, Janos | |
| dc.creator | Juhasz, Istvan | |
| dc.creator | Soukup, Lajos | |
| dc.creator | Szentmiklossy, Zoltan | |
| dc.date | 2002-04-10 | |
| dc.date.accessioned | 2026-07-07T04:47:34Z | |
| dc.date.available | 2026-07-07T04:47:34Z | |
| dc.description | Let us call a function $f$ from a space $X$ into a space $Y$ preserving if the image of every compact subspace of $X$ is compact in $Y$ and the image of every connected subspace of $X$ is connected in $Y$. By elementary theorems a continuous function is always preserving. Evelyn R. McMillan proved in 1970 that if $X$ is Hausdorff, locally connected and Frechet, $Y$ is Hausdorff, then the converse is also true: any preserving function $f:X\to Y$ is continuous. The main result of this paper is that if $X$ is any product of connected linearly ordered spaces (e.g. if $X = R^κ$) and $f:X \to Y$ is a preserving function into a regular space $Y$, then $f$ is continuous. | |
| dc.description | 26 pages. This article has been submitted for publication to Fundamenta Mathematicae | |
| dc.identifier | https://arxiv.org/abs/math/0204125 | |
| dc.identifier | http://arxiv.org/abs/math/0204125 | |
| dc.identifier | Proceedings of the Ninth Prague Topological Symposium, (Prague, 2001), pp. 93--118, Topology Atlas, Toronto, 2002 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63768 | |
| dc.subject | General Topology | |
| dc.subject | 54C05, 54D05, 54F05, 54B10 | |
| dc.title | Characterizing continuity by preserving compactness and connectedness | |
| dc.type | text |