Products and measurable cardinals
Szymański, Andrzej (1985)
Proceedings of the 13th Winter School on Abstract Analysis
János Gerlits, Zsigmond Nagy (1982)
Commentationes Mathematicae Universitatis Carolinae
Obersnel, Franco, Tironi, Gino (1995)
Mathematica Pannonica
Samuel Gomes da Silva (2005)
Commentationes Mathematicae Universitatis Carolinae
Generalizations of earlier negative results on Property are proved and two questions on an -version of Jones’ Lemma are posed. We discuss these questions in the realm of locally compact spaces. Using dominating families of functions as a tool, we prove that under the assumptions “ is regular” and “” the existence of a separable locally compact -space with an uncountable closed discrete subset implies the existence of inner models with measurable cardinals. We also use cardinal invariants...
W. Kulpa (1975)
Fundamenta Mathematicae
Roberto Pichardo-Mendoza, Angel Tamariz-Mascarúa, Humberto Villegas-Rodríguez (2013)
Commentationes Mathematicae Universitatis Carolinae
Given a Tychonoff space , a base for an ideal on is called pseudouniform if any sequence of real-valued continuous functions which converges in the topology of uniform convergence on converges uniformly to the same limit. This paper focuses on pseudouniform bases for ideals with particular emphasis on the ideal of compact subsets and the ideal of all countable subsets of the ground space.
Ljubiša Kočinac (1983)
Publications de l'Institut Mathématique
Bukovský, L., Copláková, E. (1982)
Proceedings of the 10th Winter School on Abstract Analysis
Giuseppe de Marco (1973)
Rendiconti del Seminario Matematico della Università di Padova
Neil Hindman, W.W. Comfort (1976)
Mathematische Zeitschrift
Lucia R. Junqueira, Alberto M. E. Levi (2015)
Commentationes Mathematicae Universitatis Carolinae
We say that a cardinal function reflects an infinite cardinal , if given a topological space with , there exists with . We investigate some problems, discussed by Hodel and Vaughan in Reflection theorems for cardinal functions, Topology Appl. 100 (2000), 47–66, and Juhász in Cardinal functions and reflection, Topology Atlas Preprint no. 445, 2000, related to the reflection for the cardinal functions character and pseudocharacter. Among other results, we present some new equivalences with...
Alan Dow, Klaas Pieter Hart (2014)
Fundamenta Mathematicae
We deal with a conjectured dichotomy for compact Hausdorff spaces: each such space contains a non-trivial converging ω-sequence or a non-trivial converging ω₁-sequence. We establish that this dichotomy holds in a variety of models; these include the Cohen models, the random real models and any model obtained from a model of CH by an iteration of property K posets. In fact in these models every compact Hausdorff space without non-trivial converging ω₁-sequences is first-countable and, in addition,...
Vladimir Tkachuk (2012)
Open Mathematics
Given a topological property P, we study when it reflects in small continuous images, i.e., when for some infinite cardinal κ, a space X has P if and only if all its continuous images of weight less or equal to κ have P. We say that a cardinal invariant η reflects in continuous images of weight κ + if η(X) ≤ κ provided that η(Y) ≤ κ whenever Y is a continuous image of X of weight less or equal to κ +. We establish that, for any infinite cardinal κ, the spread, character, pseudocharacter and Souslin...
István Juhász, Lajos Soukup, Zoltán Szentmiklóssy (2015)
Fundamenta Mathematicae
We improve some results of Pavlov and Filatova, concerning a problem of Malykhin, by showing that every regular space X that satisfies Δ(X) > e(X) is ω-resolvable. Here Δ(X), the dispersion character of X, is the smallest size of a non-empty open set in X, and e(X), the extent of X, is the supremum of the sizes of all closed-and-discrete subsets of X. In particular, regular Lindelöf spaces of uncountable dispersion character are ω-resolvable. We also prove that any regular...
Z. Balogh (1978)
Fundamenta Mathematicae
A. V. Arhangel'skii (2013)
Fundamenta Mathematicae
We continue the study of remainders of metrizable spaces, expanding and applying results obtained in [Fund. Math. 215 (2011)]. Some new facts are established. In particular, the closure of any countable subset in the remainder of a metrizable space is a Lindelöf p-space. Hence, if a remainder of a metrizable space is separable, then this remainder is a Lindelöf p-space. If the density of a remainder Y of a metrizable space does not exceed , then Y is a Lindelöf Σ-space. We also show that many of...
Hernández T., Nelson C. (1998)
Divulgaciones Matemáticas
Kazushi Yoshitomi (2021)
Mathematica Bohemica
We extend the Noble and Ulmer theorem and the Juhász and Hajnal theorems in set-theoretic topology. We show that a statement analogous to that in the former theorem is valid for a family of almost topological convergences, whereas statements analogous to those in the latter theorems hold for a pretopologically Hausdorff convergence.
Stevo Todorčević (1986)
Compositio Mathematica
Stevo Todorčević (1985)
Compositio Mathematica