A connection between multiplication in C(X) and the dimension of X

Andrzej Komisarski. "A connection between multiplication in C(X) and the dimension of X." Fundamenta Mathematicae 189.2 (2006): 149-154. <http://eudml.org/doc/286633>.

@article{AndrzejKomisarski2006,
abstract = {Let X be a compact Hausdorff topological space. We show that multiplication in the algebra C(X) is open iff dim X < 1. On the other hand, the existence of non-empty open sets U,V ⊂ C(X) satisfying Int(U· V) = ∅ is equivalent to dim X > 1. The preimage of every set of the first category in C(X) under the multiplication map is of the first category in C(X) × C(X) iff dim X ≤ 1.},
author = {Andrzej Komisarski},
journal = {Fundamenta Mathematicae},
keywords = {weakly open map; function algebra; topological dimension},
language = {eng},
number = {2},
pages = {149-154},
title = {A connection between multiplication in C(X) and the dimension of X},
url = {http://eudml.org/doc/286633},
volume = {189},
year = {2006},
}

TY - JOUR
AU - Andrzej Komisarski
TI - A connection between multiplication in C(X) and the dimension of X
JO - Fundamenta Mathematicae
PY - 2006
VL - 189
IS - 2
SP - 149
EP - 154
AB - Let X be a compact Hausdorff topological space. We show that multiplication in the algebra C(X) is open iff dim X < 1. On the other hand, the existence of non-empty open sets U,V ⊂ C(X) satisfying Int(U· V) = ∅ is equivalent to dim X > 1. The preimage of every set of the first category in C(X) under the multiplication map is of the first category in C(X) × C(X) iff dim X ≤ 1.
LA - eng
KW - weakly open map; function algebra; topological dimension
UR - http://eudml.org/doc/286633
ER -