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Cardinal invariants of universals

Gareth Fairey, Paul Gartside, Andrew Marsh (2005)

Commentationes Mathematicae Universitatis Carolinae

We examine when a space $X$ has a zero set universal parametrised by a metrisable space of minimal weight and show that this depends on the $σ$ -weight of $X$ when $X$ is perfectly normal. We also show that if $Y$ parametrises a zero set universal for $X$ then $h L (X^{n}) \leq h d (Y)$ for all $n \in ℕ$ . We construct zero set universals that have nice properties (such as separability or ccc) in the case where the space has a $K$ -coarser topology. Examples are given including an $S$ space with zero set universal parametrised by an $L$ space (and...

Compact-like properties in hyperspaces

J. Angoa, Y. F. Ortiz-Castillo, Á. Tamariz-Mascarúa (2013)

Matematički Vesnik

Constructing Banaschewski compactification without Dedekind completeness axiom.

Acharyya, S.K., Chattopadhyay, K.C., Ghosh, Partha Pratim (2004)

International Journal of Mathematics and Mathematical Sciences

Continuous images of $N^{}$ which are homeomorphic to $N^{}$ .

Mawhinney, K.J., Vipera, M.C. (2005)

Mathematica Pannonica

Coronas of ultrametric spaces

Igor V. Protasov (2011)

Commentationes Mathematicae Universitatis Carolinae

We show that, under CH, the corona of a countable ultrametric space is homeomorphic to $ω^{*}$ . As a corollary, we get the same statements for the Higson’s corona of a proper ultrametric space and the space of ends of a countable locally finite group.

Countable Compact Scattered T₂ Spaces and Weak Forms of AC

Kyriakos Keremedis, Evangelos Felouzis, Eleftherios Tachtsis (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

We show that: (1) It is provable in ZF (i.e., Zermelo-Fraenkel set theory minus the Axiom of Choice AC) that every compact scattered T₂ topological space is zero-dimensional. (2) If every countable union of countable sets of reals is countable, then a countable compact T₂ space is scattered iff it is metrizable. (3) If the real line ℝ can be expressed as a well-ordered union of well-orderable sets, then every countable compact zero-dimensional T₂ space...

Countable dense homogeneous filters and the Menger covering property

Dušan Repovš, Lyubomyr Zdomskyy, Shuguo Zhang (2014)

Fundamenta Mathematicae

We present a ZFC construction of a non-meager filter which fails to be countable dense homogeneous. This answers a question of Hernández-Gutiérrez and Hrušák. The method of the proof also allows us to obtain for any n ∈ ω ∪ {∞} an n-dimensional metrizable Baire topological group which is strongly locally homogeneous but not countable dense homogeneous.