3 citations · 9 across the 17 of their papers we have counts for
19 papers · 1 filter
Spaces of countable free set number and PFA
Alan Dow, Istvan Juhasz
The main result of this paper is that, under PFA, for every {\em regular} space with we have ; in particular, implies $|X| \l…
On a problem of Angelo Bella
Istvan Juhasz, Lajos Soukup, Zoltan Szentmiklossy
The main result of this note is the following theorem. "If is any Hausdorff space with then ". Here $\widehat{…
The double density spectrum of a topological space
Istvan Juhasz, Jan van Mill, Lajos Soukup +1
It is an interesting, maybe surprising, fact that different dense subspaces of even "nice" topological spaces can have different densities. So, our aim here is to investigate the s…
On the cardinality of separable pseudoradial spaces
Alan Dow, Istvan Juhasz
The aim of this paper is to consider questions concerning the possible maximum cardinality of various separable pseudoradial (in short: SP) spaces. The most intriguing question her…
Densely k-separable compacta are densely separable
Alan Dow, Istvan Juhasz
A space has -compact tightness if the closures of -compact subsets determines the topology. We consider a dense set variant that we call densely k-separable. We consider the…
On the tightness of -modifications
Alan Dow, István Juhász, Lajos Soukup +2
The -modification of a topological space is the space on the same underlying set generated by, i.e. having as a basis, the collection of all subsets of . Be…
Weakly linearly Lindelöf monotonically normal spaces are Lindelöf
I. Juhász, V. V. Tkachuk, R. G. Wilson
We call a space {\it weakly linearly Lindelöf} if for any family of non-empty open subsets of of regular uncountable cardinality , there exists a point $x\…
On -countably tight spaces
István Juhász, Jan van Mill
Extending a result of R. de la Vega, we prove that an infinite homogeneous compactum has cardinality if either it is the union of countably many dense or finitely ma…
Pinning Down versus Density
István Juhász, Lajos Soukup, Zoltán Szentmiklóssy
The pinning down number of a topological space is the smallest cardinal such that for any neighborhood assignment there is a set with $…
Regular spaces of small extent are omega-resolvable
Istvan Juhasz, Lajos Soukup, Zoltan Szentmiklossy
We improve some results of Pavlov and of Filatova, respectively, concerning a problem of Malychin by showing that every regular space X that satisfies Delta(X)>ext(X) is omega-reso…
Strong colorings yield kappa-bounded spaces with discretely untouchable points
Istvan Juhasz, Saharon Shelah
It is well-known that every non-isolated point in a compact Hausdorff space is the accumulation point of a discrete subset. Answering a question raised by Z. Szentmiklossy and the…
CH, a problem of Rolewicz and bidiscrete systems
MIrna Dzamonja, Istvan Juhasz
We give a construction under of a non-metrizable compact Hausdorff space such that any uncountable semi-biorthogonal sequence in must be of a very specific kind. Th…
Projective -character bounds the order of a -base
Istvan Juhasz, Zoltan Szentmiklossy
All spaces below are Tychonov. We define the projective pi-character p(X) of a space X as the supremum of the values where Y ranges over all continuous images of X. Our mai…
First countable spaces without point-countable -base
Istvan Juhasz, Lajos Soukup, Zoltan Szentmiklossy
We answer several questions of V. Tkačuk from [Point-countable -bases in first countable and similar spaces, Fund. Math. 186 (2005), pp. 55--69.] by showing that (1) there is a…
Resolvability vs. almost resolvability
Istvan Juhasz, Saharon Shelah, Lajos Soukup
A space X is kappa-resolvable (resp. almost kappa-resolvable) if it contains kappa dense sets that are pairwise disjoint (resp. almost disjoint over the ideal of nowhere dense subs…
Resolvability and monotone normality
Istvan Juhasz, Lajos Soukup, Zoltan Szentmiklossy
A space is said to be -resolvable (resp. almost -resolvable) if it contains dense sets that are pairwise disjoint (resp. almost disjoint over the ideal of nowhere den…
Resolvability of spaces having small spread or extent
Istvan Juhasz, Lajos Soukup, Zoltan Szentmiklossy
In a recent paper O. Pavlov proved the following two interesting resolvability results: (1) If a space satisfies $Δ(X) > \ps(X)$ then is maximally resolvable. (2) If a $T_3…
D-forced spaces: a new approach to resolvability
Istvan Juhasz, Lajos Soukup, Zoltan Szentmiklossy
We introduce a ZFC method that enables us to build spaces (in fact special dense subspaces of certain Cantor cubes) in which we have "full control" over all dense subsets. Using th…
Characterizing continuity by preserving compactness and connectedness
Janos Gerlits, Istvan Juhasz, Lajos Soukup +1
Let us call a function from a space into a space preserving if the image of every compact subspace of is compact in and the image of every connected subspace of…