Disconnectedness properties of hyperspaces

Rodrigo Hernández-Gutiérrez; Angel Tamariz-Mascarúa

An independency result in connectification theory

Alessandro Fedeli, Attilio Le Donne (1999)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

A space is called connectifiable if it can be densely embedded in a connected Hausdorff space. Let $ψ$ be the following statement: “a perfect $T_{3}$ -space $X$ with no more than $2^{𝔠}$ clopen subsets is connectifiable if and only if no proper nonempty clopen subset of $X$ is feebly compact". In this note we show that neither $ψ$ nor $\neg ψ$ is provable in ZFC.

The regular topology on $C (X)$

Wolf Iberkleid, Ramiro Lafuente-Rodriguez, Warren Wm. McGovern (2011)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Hewitt [Rings of real-valued continuous functions. I., Trans. Amer. Math. Soc. 64 (1948), 45–99] defined the $m$ -topology on $C (X)$ , denoted $C_{m} (X)$ , and demonstrated that certain topological properties of $X$ could be characterized by certain topological properties of $C_{m} (X)$ . For example, he showed that $X$ is pseudocompact if and only if $C_{m} (X)$ is a metrizable space; in this case the $m$ -topology is precisely the topology of uniform convergence. What is interesting with regards to the $m$ -topology is that it is...

Displaying similar documents to “Disconnectedness properties of hyperspaces”

An independency result in connectification theory

The regular topology on C ( X )

The regular topology on $C (X)$