Detail publikace

On Mutual Compactificability and Compactificability Classes

KOVÁR, M.

Originální název

On Mutual Compactificability and Compactificability Classes

Typ

článek ve sborníku ve WoS nebo Scopus

Jazyk

angličtina

Originální abstrakt

\abstract Conceived intuitively, various topological spaces undoubtedly have different degrees of ``compactness'' or ``non-compactness''. But how to practically determine whether some space is more non-compact than the other? In this work the main criterion of the ``level of non-compactness'' of a topological space $X$ is its ability to form, together with another space $Y$, a compact space $K=X\cup Y$ such that the points of $X$ are in $K$ separated from the points of $Y$ by disjoint open neighbourhoods. Noticing that the existence of such topology on $K$ implies $\theta$-regularity of both $X$ and $Y$, at the background of these considerations lies the idea to imagine the compact space as a box of bricks or jigsaw puzzle where ``bricks'' or ``pieces'' are certain $\theta$-regular spaces. The principal problem is which ``pieces'' are so compatible that they together can create some compact space. For simplicity, accepting the jigsaw model, in this work we will deal with puzzles of two pieces. Since finding a general applicable criterion of such compatibility of $\theta$-regular spaces (``bricks'' or ``pieces'') is a difficult problem, we will proceed indirectly. We will compare different spaces in their behaviour with respect to the above criterion and join together to one class the spaces whose behaviour is similar. After testing on the real line, we obtain that any non-compact locally connected metrizable generalized continuum as well as Cantor space without its ``left corner'' $\Bbb D^{\aleph_0}\smallsetminus \left\{\boldkey 0\right\}$ are of the same class of mutual compactificability as $\Bbb R$.

Klíčová slova

compact space, compactification, $\theta$-regular space

Autoři

KOVÁR, M.

Vydáno

23. 8. 1996

Nakladatel

Topology Atlas

Strany od

173

Strany do

177

Strany počet

5

URL

BibTex

@inproceedings{BUT6909,
  author="Martin {Kovár}",
  title="On Mutual Compactificability and Compactificability Classes",
  booktitle="Proceedings of the Eighth Prague Topological Symposium",
  year="1996",
  volume="1996",
  number="1",
  pages="5",
  publisher="Topology Atlas",
  url="http://at.yorku.ca/p/p/a/b/04.htm"
}