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Displaying 61 – 72 of 72

On typical parametrizations of finite-dimensional compacta on the Cantor set

Paweł Milewski (2002)

Fundamenta Mathematicae

We prove that if X is a perfect finite-dimensional compactum, then for almost every continuous surjection of the Cantor set onto X, the set of points of maximal order is uncountable. Moreover, if X is a perfect compactum of positive finite dimension then for a typical parametrization of X on the Cantor set, the set of points of maximal order is homeomorphic to the product of the rationals and the Cantor set.

On unified theory for continuities.

Küçük, Mahide, Küçük, Yalçin (2002)

International Journal of Mathematics and Mathematical Sciences

On weaker forms of compactness, Lindelöfness, and countable compactness.

Baboolal, D., Backhouse, J., Ori, R.G. (1990)

International Journal of Mathematics and Mathematical Sciences

On $β$ - $I$ -open sets and a decomposition of almost- $I$ -continuity.

Hatir, E., Noiri, T. (2006)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

On $θ$ -closed sets and some forms of continuity

Mohammad Saleh (2004)

Archivum Mathematicum

In this paper, we further the study of $θ$ -compactness a generalization of quasi-H-closed sets and its applications to some forms of continuity using $θ$ -open and $δ$ -open sets. Among other results, it is shown a weakly $θ$ -retract of a Hausdorff space $X$ is a $δ$ -closed subset of $X$ .

On $θ$ -continuity and strong $θ$ -continuity.

Saleh, Mohammed (2003)

Applied Mathematics E-Notes [electronic only]

On $Θ$ -regular spaces.

Kovár, Martin M. (1994)

International Journal of Mathematics and Mathematical Sciences

Onto Gelfand maps : appendix

Brian J. Day (1989)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Opérations de Hausdorff itérées et réunions croissantes de compacts

Sylvain Kahane (1992)

Fundamenta Mathematicae

In this paper, motivated by questions in Harmonic Analysis, we study the operation of (countable) increasing union, and show it is not idempotent: $ω_{1}$ iterations are needed in general to obtain the closure of a class under this operation. Increasing union is a particular Hausdorff operation, and we present the combinatorial tools which allow to study the power of various Hausdorff operations, and of their iterates. Besides countable increasing union, we study in detail a related Hausdorff operation,...

Operator compactification of topological spaces.

Rosas, Ennis, Vielma, Jorge (2000)

Divulgaciones Matemáticas

Order intervals in $C (K)$ . Compactness, coincidence of topologies, metrizability

Zbigniew Lipecki (2022)

Commentationes Mathematicae Universitatis Carolinae

Let $K$ be a compact space and let $C (K)$ be the Banach lattice of real-valued continuous functions on $K$ . We establish eleven conditions equivalent to the strong compactness of the order interval $[0, x]$ in $C (K)$ , including the following ones: (i) ${x > 0}$ consists of isolated points of $K$ ; (ii) $[0, x]$ is pointwise compact; (iii) $[0, x]$ is weakly compact; (iv) the strong topology and that of pointwise convergence coincide on $[0, x]$ ; (v) the strong and weak topologies coincide on $[0, x]$ . Moreover, the weak topology and that of pointwise convergence...

Order-like structure of monotonically normal spaces

Scott W. Williams, Hao Xuan Zhou (1998)

Commentationes Mathematicae Universitatis Carolinae

For a compact monotonically normal space X we prove: (1) $X$ has a dense set of points with a well-ordered neighborhood base (and so $X$ is co-absolute with a compact orderable space); (2) each point of $X$ has a well-ordered neighborhood $π$ -base (answering a question of Arhangel’skii); (3) $X$ is hereditarily paracompact iff $X$ has countable tightness. In the process we introduce weak-tightness, a notion key to the results above and yielding some cardinal function results on monotonically normal...

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