All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 4 Next

Displaying 61 – 80 of 107

Showing per page

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 results and problems about weakly pseudocompact spaces

Oleg Okunev, Angel Tamariz-Mascarúa (2000)

Commentationes Mathematicae Universitatis Carolinae

A space X is truly weakly pseudocompact if X is either weakly pseudocompact or Lindelöf locally compact. We prove: (1) every locally weakly pseudocompact space is truly weakly pseudocompact if it is either a generalized linearly ordered space, or a proto-metrizable zero-dimensional space with χ ( x , X ) > ω for every x ∈ X ; (2) every locally bounded space is truly weakly pseudocompact; (3) for ω < κ < α , the κ -Lindelöfication of a discrete space of cardinality α is weakly pseudocompact if κ = κ ω .

Spaces of continuous characteristic functions

Raushan Z. Buzyakova (2006)

Commentationes Mathematicae Universitatis Carolinae

We show that if X is first-countable, of countable extent, and a subspace of some ordinal, then C p ( X , 2 ) is Lindelöf.

Spaces of continuous functions, box products and almost- ω -resolvable spaces

Angel Tamariz-Mascarúa, H. Villegas-Rodríguez (2002)

Commentationes Mathematicae Universitatis Carolinae

A dense-in-itself space X is called C □ -discrete if the space of real continuous functions on X with its box topology, C □ ( X ) , is a discrete space. A space X is called almost- ω -resolvable provided that X is the union of a countable increasing family of subsets each of them with an empty interior. We analyze these classes of spaces by determining their relations with κ -resolvable and almost resolvable spaces. We prove that every almost- ω -resolvable space is C □ -discrete, and that these classes coincide in...

Spaces of continuous step functions over LOTS

Raushan Z. Buzyakova (2006)

Fundamenta Mathematicae

We investigate spaces C p ( · , n ) over LOTS (linearly ordered topological spaces). We find natural necessary conditions for linear Lindelöfness of C p ( · , n ) over LOTS. We also characterize countably compact LOTS whose C p ( · , n ) is linearly Lindelöf for each n. Both the necessary conditions and the characterization are given in terms of the topology of the Dedekind completion of a LOTS.

Spaces of σ-finite linear measure

Ihor Stasyuk, Edward D. Tymchatyn (2013)

Colloquium Mathematicae

Spaces of finite n-dimensional Hausdorff measure are an important generalization of n-dimensional polyhedra. Continua of finite linear measure (also called continua of finite length) were first characterized by Eilenberg in 1938. It is well-known that the property of having finite linear measure is not preserved under finite unions of closed sets. Mauldin proved that if X is a compact metric space which is the union of finitely many closed sets each of which admits a σ-finite linear measure then...

Currently displaying 61 – 80 of 107