Record number :

1576320

Title of article :

Functional equivalence of topological spaces

Author/Authors :

Choban، نويسنده , , M.M.، نويسنده ,

Issue Information :

دوماهنامه با شماره پیاپی سال 2001

Pages :

30

From page :

105

To page :

134

Abstract :

Let E be a non-trivial Banach space. The question when the spaces Cp(X,E) and Cp(Y,E) of all continuous mappings of X and Y into E in the topology of pointwise convergence are linearly homeomorphic is studied. These spaces are called lE-equivalent. A topological property or a cardinal function is called lE-invariant if it is preserved by the relation of the lE-equivalence. We prove that σ-discreteness, σ-scatteredness, the hereditary Lindelöf number, the hereditary density, the density, and the spread are lE-invariant properties. Moreover, we prove that in the class of μ-spaces of pointwise countable type the scatteredness, k-scatteredness, the extent, the paracompactness, and the p-paracompactness are lE-invariants. For that we introduce the notions of pm-equivalence, om-equivalence, pom-equivalence. We study some functional functors.

Keywords :

Functional functor , Set-Valued Mapping , Topological equivalence , Scattered space , Extender , Function space

Journal title :

Topology and its Applications

Journal title :

Topology and its Applications

Serial Year :

2001

Link To Document :