Hereditarily Hurewicz spaces and Arhangel'skii sheaf amalgamations

Tsaban, Boaz, and Zdomsky, Lubomyr. "Hereditarily Hurewicz spaces and Arhangel'skii sheaf amalgamations." Journal of the European Mathematical Society 014.2 (2012): 353-372. <http://eudml.org/doc/277316>.

@article{Tsaban2012,
abstract = {A classical theorem of Hurewicz characterizes spaces with the Hurewicz covering property as those having bounded continuous images in the Baire space. We give a similar characterization for spaces $X$ which have the Hurewicz property hereditarily. We proceed to consider the class of Arhangel’skii $\alpha _1$ spaces, for which every sheaf at a point can be amalgamated in a natural way. Let $C_p(X)$ denote the space of continuous real-valued functions on $X$ with the topology of pointwise convergence. Our main result is that $C_p(X)$ is an $\sigma _1$ space if, and only if, each Borel image of $X$ in the Baire space is bounded. Using this characterization, we solve a variety of problems posed in the literature concerning spaces of continuous functions.},
author = {Tsaban, Boaz, Zdomsky, Lubomyr},
journal = {Journal of the European Mathematical Society},
keywords = {pointwise convergence; point-cofinite covers; $\alpha _1$; eventual dominance; Hurewicz property; selection principles; QN sets; ideal convergence; pointwise convergence; point-cofinite covers; space; eventual dominance; Hurewicz property; selection principles; QN sets; ideal convergence},
language = {eng},
number = {2},
pages = {353-372},
publisher = {European Mathematical Society Publishing House},
title = {Hereditarily Hurewicz spaces and Arhangel'skii sheaf amalgamations},
url = {http://eudml.org/doc/277316},
volume = {014},
year = {2012},
}

TY - JOUR
AU - Tsaban, Boaz
AU - Zdomsky, Lubomyr
TI - Hereditarily Hurewicz spaces and Arhangel'skii sheaf amalgamations
JO - Journal of the European Mathematical Society
PY - 2012
PB - European Mathematical Society Publishing House
VL - 014
IS - 2
SP - 353
EP - 372
AB - A classical theorem of Hurewicz characterizes spaces with the Hurewicz covering property as those having bounded continuous images in the Baire space. We give a similar characterization for spaces $X$ which have the Hurewicz property hereditarily. We proceed to consider the class of Arhangel’skii $\alpha _1$ spaces, for which every sheaf at a point can be amalgamated in a natural way. Let $C_p(X)$ denote the space of continuous real-valued functions on $X$ with the topology of pointwise convergence. Our main result is that $C_p(X)$ is an $\sigma _1$ space if, and only if, each Borel image of $X$ in the Baire space is bounded. Using this characterization, we solve a variety of problems posed in the literature concerning spaces of continuous functions.
LA - eng
KW - pointwise convergence; point-cofinite covers; $\alpha _1$; eventual dominance; Hurewicz property; selection principles; QN sets; ideal convergence; pointwise convergence; point-cofinite covers; space; eventual dominance; Hurewicz property; selection principles; QN sets; ideal convergence
UR - http://eudml.org/doc/277316
ER -