On a construction of perfectly normal spaces and its applications to dimension theory
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Gary Gruenhage, Elżbieta Pol (1983)
Fundamenta Mathematicae
Gary Gruenhage (1986)
Fundamenta Mathematicae
John Martin (1976)
Fundamenta Mathematicae
Sergei Logunov (2022)
Commentationes Mathematicae Universitatis Carolinae
Let be the Tychonoff product of -many Tychonoff non-single point spaces . Let be a point in the closure of some whose weak Lindelöf number is strictly less than the cofinality of . Then we show that is not normal. Under some additional assumptions, is a butterfly-point in . In particular, this is true if either or and is infinite and not countably cofinal.
Gerald Kuba (2012)
Matematički Vesnik
Jan van Mill (2005)
Bulletin of the Polish Academy of Sciences. Mathematics
We present an example of a connected, Polish, countable dense homogeneous space X that is not strongly locally homogeneous. In fact, a nontrivial homeomorphism of X is the identity on no nonempty open subset of X.
Matyushichev, K.V. (2000)
Siberian Mathematical Journal
A. Hajnal, Istvan Juhász (1974)
Fundamenta Mathematicae
Sergei Logunov (2021)
Commentationes Mathematicae Universitatis Carolinae
We show that is not normal, if is a limit point of some countable subset of , consisting of points of character . Moreover, such a point is a Kunen point and a super Kunen point.
Marta N. Charatonik, Włodzimierz J. Charatonik (2000)
Commentationes Mathematicae Universitatis Carolinae
A Mazurkiewicz set is a subset of a plane with the property that each straight line intersects in exactly two points. We modify the original construction to obtain a Mazurkiewicz set which does not contain vertices of an equilateral triangle or a square. This answers some questions by L.D. Loveland and S.M. Loveland. We also use similar methods to construct a bounded noncompact, nonconnected generalized Mazurkiewicz set.
Sergei Logunov (2022)
Commentationes Mathematicae Universitatis Carolinae
Let a space be Tychonoff product of -many Tychonoff nonsingle point spaces . Let Suslin number of be strictly less than the cofinality of . Then we show that every point of remainder is a non-normality point of its Čech–Stone compactification . In particular, this is true if is either or and a cardinal is infinite and not countably cofinal.
Ali A. Fora, Hasan Z. Hdeib (1983)
Revista colombiana de matematicas
M. Sanchis, A. Tamariz-Mascarúa (1999)
Colloquium Mathematicae
The notion of quasi-p-boundedness for p ∈ is introduced and investigated. We characterize quasi-p-pseudocompact subsets of β(ω) containing ω, and we show that the concepts of RK-compatible ultrafilter and P-point in can be defined in terms of quasi-p-pseudocompactness. For p ∈ , we prove that a subset B of a space X is quasi-p-bounded in X if and only if B × is bounded in X × , if and only if , where is the set of Rudin-Keisler predecessors of p.
T. Maćkowiak (1975)
Fundamenta Mathematicae
Andrzej Szymański (1982)
Colloquium Mathematicae
Sergei Logunov (2022)
Commentationes Mathematicae Universitatis Carolinae
We discuss the following result of A. Szymański in “Retracts and non-normality points" (2012), Corollary 3.5.: If is a closed subspace of and the -weight of is countable, then every nonisolated point of is a non-normality point of . We obtain stronger results for all types of points, excluding the limits of countable discrete sets considered in “Some non-normal subspaces of the Čech–Stone compactification of a discrete space” (1980) by A. Błaszczyk and A. Szymański. Perhaps our proofs...
Salvador García-Ferreira, Yackelin Rodríguez-López, Carlos Uzcátegui (2021)
Commentationes Mathematicae Universitatis Carolinae
We consider discrete dynamical systems whose phase spaces are compact metrizable countable spaces. In the first part of the article, we study some properties that guarantee the continuity of all functions of the corresponding Ellis semigroup. For instance, if every accumulation point of is fixed, we give a necessary and sufficient condition on a point in order that all functions of the Ellis semigroup be continuous at the given point . In the second part, we consider transitive dynamical...
Umed Karimov, Dušan Repovš (2012)
Open Mathematics
We calculate the singular homology and Čech cohomology groups of the Harmonic Archipelago. As a corollary, we prove that this space is not homotopy equivalent to the Griffiths space. This is interesting in view of Eda’s proof that the first singular homology groups of these spaces are isomorphic.
Dušan Repovš, Arkadij Skopenkov, Evgenij Ščepin (1996)
Colloquium Mathematicae
We prove that if the Euclidean plane contains an uncountable collection of pairwise disjoint copies of a tree-like continuum X, then the symmetric span of X is zero, sX = 0. We also construct a modification of the Oversteegen-Tymchatyn example: for each ε > 0 there exists a tree such that σX < ε but X cannot be covered by any 1-chain. These are partial solutions of some well-known problems in continua theory.
Pelant, Jan, Pták, Pavel (1976)
Seminar Uniform Spaces
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