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Topological compactifications

100%

Vejnar B.

Fundamenta Mathematicae

2011

tom 213

nr 3

233-253

We study those compactifications of a space such that every autohomeomorphism of the space can be continuously extended over the compactification. These are called H-compactifications. Van Douwen proved that there are exactly three H-compactifications of the real line. We prove that there exist only two H-compactifications of Euclidean spaces of higher dimension. Next we show that there are 26 H-compactifications of a countable sum of real lines and 11 H-compactifications of a countable sum of Euclidean spaces of higher dimension. All H-compactifications of discrete and countable locally compact spaces are described.

Waraszkiewicz spirals revisited

63%

Pyrih P., Vejnar B.

Fundamenta Mathematicae

2012

tom 219

nr 2

97-104

We study compactifications of a ray with remainder a simple closed curve. We give necessary and sufficient conditions for the existence of a bijective (resp. surjective) mapping between two such continua. Using those conditions we present a simple proof of the existence of an uncountable family of plane continua no one of which can be continuously mapped onto any other (the first such family, so called Waraszkiewicz's spirals, was created by Z. Waraszkiewicz in the 1930's).

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2 Fundamenta Mathematicae

2 Vejnar B.

1 Pyrih P.

1 2012

1 2011

Wyniki wyszukiwania

Topological compactifications

Waraszkiewicz spirals revisited