On subsets of Alexandroff duplicates

Takemi Mizokami

Displaying similar documents to “On subsets of Alexandroff duplicates”

Perfect pre-images of cofinally complete metric spaces

Adalberto García-Máynez, Salvador Romaguera (1999)

Commentationes Mathematicae Universitatis Carolinae

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We show that a Tychonoff space is the perfect pre-image of a cofinally complete metric space if and only if it is paracompact and cofinally Čech complete. Further properties of these spaces are discussed. In particular, cofinal Čech completeness is preserved both by perfect mappings and by continuous open mappings.

Rectangular covers of products missing diagonals

Yukinobu Yajima (1994)

Commentationes Mathematicae Universitatis Carolinae

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We give a characterization of a paracompact $Σ$ -space to have a $G_{δ}$ -diagonal in terms of three rectangular covers of $X^{2} ∖ Δ$ . Moreover, we show that a local property and a global property of a space $X$ are given by the orthocompactness of $(X \times β X) ∖ Δ$ .

A note on monotone countable paracompactness

Ge Ying, Chris Good (2001)

Commentationes Mathematicae Universitatis Carolinae

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We show that a space is MCP (monotone countable paracompact) if and only if it has property $(*)$ , introduced by Teng, Xia and Lin. The relationship between MCP and stratifiability is highlighted by a similar characterization of stratifiability. Using this result, we prove that MCP is preserved by both countably biquotient closed and peripherally countably compact closed mappings, from which it follows that both strongly Fréchet spaces and q-space closed images of MCP spaces are MCP. Some...