Displaying similar documents to “On some covering properties of metric spaces”

Complete Spaces

Karol Pąk (2008)

Formalized Mathematics

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This paper is a continuation of [12]. First some definitions needed to formulate Cantor's theorem on complete spaces and show several facts about them are introduced. Next section contains the proof of Cantor's theorem and some properties of complete spaces resulting from this theorem. Moreover, countable compact spaces and proofs of auxiliary facts about them is defined. I also show the important condition that every metric space is compact if and only if it is countably compact. Then...

On metric σ-discrete spaces

Szymon Plewik, Marta Walczyńska (2016)

Banach Center Publications

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By studying dimensional types of metric scattered spaces, we consider the wider class of metric σ-discrete spaces. Applying techniques relevant to this wider class, we present new proofs of some embeddable properties of countable metric spaces in such a way that they can be generalized onto uncountable metric scattered spaces. Related topics are also explored, which gives a few new results.