Zerofree extension of continuous functions on a compact Hausdorff space

On images of continuous functions from a compact manifold to Euclidean space

Continuous Functions on Products of Compact Hausdorff Spaces

In the original version of the present paper submitted in 1995, we stated: "As far as we know it may be possible to prove that, if H and K are two compact Hausdorff spaces and (C(H), pointwise) and (C(K), pointwise) are both a-fragmented, then (C(HxK), pointwise) is also a-fragmented. If this is so, then the condition that for each finite subset O of F the space C(U {Kv: (pe}, pointwise) is ...

On the Normed Linear Space of Hausdorff Continuous Functions

In the present work we show that the linear operations in the space of Hausdorff continuous functions are generated by an extension property of these functions. We show that the supremum norm can be defined for Hausdorff continuous functions in a similar manner as for real functions, and that the space of all bounded Hausdorff continuous functions on an open set is a normed linear space. Some i...

Algebraic operations on the space of Hausdorff continuous interval functions

We show that the operations addition and multiplication on the set C(Ω) of all real continuous functions on Ω ⊆ Rn can be extended to the set H(Ω) of all Hausdorff continuous interval functions on Ω in such a way that the algebraic structure of C(Ω) is preserved, namely, H(Ω) is a commutative ring with identity. The operations on H(Ω) are defined in three different but equivalent ways. This all...

on images of continuous functions from a compact manifold to euclidean space