Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X37No. 420111215One-point extensions of locally compact paracompact spaces199228380ENM. R.KousheshJournal Article20100316A space $Y$ is called an {em extension} of a space $X$, if $Y$ <br />contains $X$ as a dense subspace. <br />Two extensions of $X$ are said to be {em equivalent}, if there is a homeomorphism between them which fixes $X$ point-wise. <br />For two (equivalence classes of) extensions $Y$ and $Y'$ of $X$ let $Yleq Y'$, if there is a continuous function of $Y'$ into $Y$ <br />which fixes $X$ point-wise. An extension $Y$ of $X$ is called a {em one-point extension}, if $Yackslash X$ is a singleton. <br />An extension $Y$ of $X$ is called {em first-countable}, if $Y$ is first-countable at points of $Yackslash X$. <br />Let ${mathcal P}$ be a topological <br />property. An extension $Y$ of $X$ is called a {em <br />${mathcal P}$-extension}, if it has ${mathcal P}$. <br /> <br /> <br />In this article, for a given locally compact paracompact space $X$, we consider the two classes of one-point v{C}ech-complete; ${mathcal P}$-extensions of $X$ and one-point first-countable locally-${mathcal P}$ extensions of $X$, and we study their order-structures, by relating them to the topology of a certain subspace of the outgrowth $eta Xackslash X$. Here ${mathcal P}$ <br />is subject to some requirements and include $sigma$-compactness and the Lindel"{o}f property as special cases.http://bims.iranjournals.ir/article_380_10262d575074c5a2c6fc9d9e59a5e26c.pdf