Displaying similar documents to “A characterization of closed maps using the Whyburn construction.”

On the subsets of non locally compact points of ultracomplete spaces

Iwao Yoshioka (2002)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

In 1998, S. Romaguera [13] introduced the notion of cofinally Čech-complete spaces equivalent to spaces which we later called ultracomplete spaces. We define the subset of points of a space X at which X is not locally compact and call it an nlc set. In 1999, Garc’ıa-Máynez and S. Romaguera [6] proved that every cofinally Čech-complete space has a bounded nlc set. In 2001, D. Buhagiar [1] proved that every ultracomplete GO-space has a compact nlc set. In this paper, ultracomplete spaces...

On absolutely submetrizable spaces

Raushan Z. Buzyakova (2006)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We introduce a notion of absolute submetrizability (= ``every Tychonoff subtopology is submetrizable'') and investigate its behavior under basic topological operations. The main result is an example of an absolutely submetrizable space that contains an uncountable set of isolated points (hence the space is neither separable nor hereditarily Lindelöf). This example is used to show that absolute submetrizability is not preserved by some topological operations, in particular, by free sums. ...