EuDML | Browse

We first provide a modified version of the proof in [3] that the Sorgenfrey line is T1. Here, we prove that it is in fact T2, a stronger result. Next, we prove that all subspaces of ℝ1 (that is the real line with the usual topology) are Lindel¨of. We utilize this result in the proof that the Sorgenfrey line is Lindel¨of, which is based on the proof found in [8]. Next, we construct the Sorgenfrey plane, as the product topology of the Sorgenfrey line and itself. We prove that the Sorgenfrey plane...

Some questions of Arhangel'skii on rotoids

Harold Bennett, Dennis Burke, David Lutzer (2012)

Fundamenta Mathematicae

A rotoid is a space X with a special point e ∈ X and a homeomorphism F: X² → X² having F(x,x) = (x,e) and F(e,x) = (e,x) for every x ∈ X. If any point of X can be used as the point e, then X is called a strong rotoid. We study some general properties of rotoids and prove that the Sorgenfrey line is a strong rotoid, thereby answering several questions posed by A. V. Arhangel'skii, and we pose further questions.

Some questions on the composition factor property for atomic mappings.

Janusz J. Charatonik (1998)

Extracta Mathematicae

Some relations between shape constructions

Friedrich W. Bauer (1978)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Some relative properties on normality and paracompactness, and their absolute embeddings

Shinji Kawaguchi, Ryoken Sokei (2005)

Commentationes Mathematicae Universitatis Carolinae

Paracompactness ( $= 2$ -paracompactness) and normality of a subspace $Y$ in a space $X$ defined by Arhangel’skii and Genedi [4] are fundamental in the study of relative topological properties ([2], [3]). These notions have been investigated by primary using of the notion of weak $C$ - or weak $P$ -embeddings, which are extension properties of functions defined in [2] or [18]. In fact, Bella and Yaschenko [8] characterized Tychonoff spaces which are normal in every larger Tychonoff space, and this result is essentially...

Some remarks about bijections onto metric spaces

Alexander P. Shostak (1984)

Czechoslovak Mathematical Journal

Some remarks on almost continuous functions

Zbigniew Piotrowski (1989)

Mathematica Slovaca

Some Remarks On Choice Topology

K. P. Chew, H. P. Tan (1972)

Publications de l'Institut Mathématique

Some remarks on choice topology.

H.P. Tan, K.P. Chew (1972)

Publications de l'Institut Mathématique [Elektronische Ressource]

Some remarks on Michael's question concerning Cartesian products of Lindelöf spaces

K. Alster (1982)

Colloquium Mathematicae

Some remarks on preservation of topological products

Luciano Stramaccia (1989)

Commentationes Mathematicae Universitatis Carolinae

Some remarks on the product of two $C_{α}$ -compact subsets

Salvador García-Ferreira, Manuel Sanchis, Stephen W. Watson (2000)

Czechoslovak Mathematical Journal

For a cardinal $α$ , we say that a subset $B$ of a space $X$ is $C_{α}$ -compact in $X$ if for every continuous function $f X \to ℝ^{α}$ , $f [B]$ is a compact subset of $ℝ^{α}$ . If $B$ is a $C$ -compact subset of a space $X$ , then $ρ (B, X)$ denotes the degree of $C_{α}$ -compactness of $B$ in $X$ . A space $X$ is called $α$ -pseudocompact if $X$ is $C_{α}$ -compact into itself. For each cardinal $α$ , we give an example of an $α$ -pseudocompact space $X$ such that $X \times X$ is not pseudocompact: this answers a question posed by T. Retta in “Some cardinal generalizations of pseudocompactness”...

Currently displaying 41 – 60 of 96

Previous Page 3 Next

Displaying 41 – 60 of 96

Some nowhere densely generated topological properties

Some problems on Suslin spaces and topological algebras

Some properties of fundamental dimension

Some properties of the functor $O_{β}$ .

Some Properties of the Sorgenfrey Line and the Sorgenfrey Plane