The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “Some properties of multiplication in the algebra C ( X ) related to the dimension of X ”

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

Andrzej Komisarski (2006)

Fundamenta Mathematicae

Similarity:

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.

Tower extension of topological constructs

De Xue Zhang (2000)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let L be a completely distributive lattice and a topological construct; a process is given in this paper to obtain a topological construct 𝐂 ( L ) , called the tower extension of 𝐂 (indexed by L ). This process contains the constructions of probabilistic topological spaces, probabilistic pretopological spaces, probabilistic pseudotopological spaces, limit tower spaces, pretopological approach spaces and pseudotopological approach spaces, etc, as special cases. It is proved that this process...