TY - JOUR
ID - 380
TI - One-point extensions of locally compact paracompact spaces
JO - Bulletin of the Iranian Mathematical Society
JA - BIMS
LA - en
SN - 1017-060X
AU - Koushesh, M. R.
AD -
Y1 - 2011
PY - 2011
VL - 37
IS - No. 4
SP - 199
EP - 228
KW - Stone-v{C}ech compactification,
one-point extension, one-point compactification, locally compact, paracompact, v{C}ech complete
KW - first-countable
DO -
N2 - A space $Y$ is called an {em extension} of a space $X$, if $Y$ contains $X$ as a dense subspace. Two extensions of $X$ are said to be {em equivalent}, if there is a homeomorphism between them which fixes $X$ point-wise. For two (equivalence classes of) extensions $Y$ and $Y'$ of $X$ let $Yleq Y'$, if there is a continuous function of $Y'$ into $Y$ which fixes $X$ point-wise. An extension $Y$ of $X$ is called a {em one-point extension}, if $Yackslash X$ is a singleton. An extension $Y$ of $X$ is called {em first-countable}, if $Y$ is first-countable at points of $Yackslash X$. Let ${mathcal P}$ be a topological property. An extension $Y$ of $X$ is called a {em ${mathcal P}$-extension}, if it has ${mathcal P}$. 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 ${mathcal P}$ is subject to some requirements and include $sigma$-compactness and the Lindel"{o}f property as special cases.
UR - http://bims.iranjournals.ir/article_380.html
L1 - http://bims.iranjournals.ir/article_380_10262d575074c5a2c6fc9d9e59a5e26c.pdf
ER -