EuDML | Browse

We consider a multifunction $F : T \times X \to 2^{E}$ , where T, X and E are separable metric spaces, with E complete. Assuming that F is jointly measurable in the product and a.e. lower semicontinuous in the second variable, we establish the existence of a selection for F which is measurable with respect to the first variable and a.e. continuous with respect to the second one. Our result is in the spirit of [11], where multifunctions of only one variable are considered.

Parametrized Cichoń's diagram and small sets

Janusz Pawlikowski, Ireneusz Recław (1995)

Fundamenta Mathematicae

We parametrize Cichoń’s diagram and show how cardinals from Cichoń’s diagram yield classes of small sets of reals. For instance, we show that there exist subsets N and M of $w^{w} \times 2^{w}$ and continuous functions $e, f : w^{w} \to w^{w}$ such that • N is $G_{δ}$ and $N_{x} : x \in w^{w}$ , the collection of all vertical sections of N, is a basis for the ideal of measure zero subsets of $2^{w}$ ; • M is $F_{σ}$ and $M_{x} : x \in w^{w}$ is a basis for the ideal of meager subsets of $2^{w}$ ; • $\forall x, y N_{e (x)} \subseteq N_{y} \Rightarrow M_{x} \subseteq M_{f (y)}$ . From this we derive that for a separable metric space X, •if for all Borel (resp. $G_{δ}$ ) sets $B \subseteq X \times 2^{w}$ with all...

Paratopological (topological) groups with certain networks

Chuan Liu (2014)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we discuss certain networks on paratopological (or topological) groups and give positive or negative answers to the questions in [Lin2013]. We also prove that a non-locally compact, $k$ -gentle paratopological group is metrizable if its remainder (in the Hausdorff compactification) is a Fréchet-Urysohn space with a point-countable cs*-network, which improves some theorems in [Liu C., Metrizability of paratopological $($ semitopological $)$ groups, Topology Appl. 159 (2012), 1415–1420], [Liu...

Partial confluence of maps onto graphs and inverse limits of single graphs

Eldon Vought, Van Nall (1991)

Fundamenta Mathematicae

Partial dcpo’s and some applications

Zhao Dongsheng (2012)

Archivum Mathematicum

We introduce partial dcpo’s and show their some applications. A partial dcpo is a poset associated with a designated collection of directed subsets. We prove that (i) the dcpo-completion of every partial dcpo exists; (ii) for certain spaces $X$ , the corresponding partial dcpo’s of continuous real valued functions on $X$ are continuous partial dcpos; (iii) if a space $X$ is Hausdorff compact, the lattice of all S-lower semicontinuous functions on $X$ is the dcpo-completion of that of continuous real valued...

Partial discretization of topologies

M. Bonanzinga, F. Cammaroto, M. V. Matveev (2000)

Bollettino dell'Unione Matematica Italiana

In questo lavoro daremo una construzione che aumenta il numero di sottospazi chiusi e discreti dello spazio e daremo alcune applicazioni di tale construzione.

Partial Fuzzy Metric Space and Some Fixed Point Results

Shaban Sedghi, Nabi Shobkolaei, Ishak Altun (2015)

Communications in Mathematics

In this paper, we introduce the concept of partial fuzzy metric on a nonempty set $X$ and give the topological structure and some properties of partial fuzzy metric space. Then some fixed point results are provided.

Currently displaying 21 – 40 of 279

Previous Page 2 Next