In this paper, we show that a pointwise symmetric pre-isotonic preclosure function is uniquely determined the pairs of sets it separates. We then show that when the preclosure function of the domain is pre-isotonic and the pre-closure function of the codomain is pre-isotonic and pointwise-pre-symmetric, functions which separate only those pairs of sets which are already separated are precontinu...

We propose a generalization of continuous lattices and domains through the concept of enriched closure space, defined as a closure space equipped with a preclosure operator satisfying some compatibility conditions. In this framework we are able to define a notion of waybelow relation; an appropriate definition of continuity then naturally follows. Characterizations of continuity of the enriched...

Let F be a monotone operator on the complete lattice L into itself. Tarski's lattice theoretical fixed point theorem states that the set of fixed points of F is a nonempty complete lattice for the ordering of L. We give a constructive proof of this theorem showing that the set of fixed points of F is the image of L by a lower and an upper preclosure operator. These preclosure operators are the ...

Challenges 2 Femoral Approach 2 Standard of Technical Excellence 2 Technique The fl uoroscopically guided micropuncture access 3 Technical Tips 4 * * Angiography to check the location of femoral entry through a dilator 4 Preparations in obese patients 4 * Directing the needle 4 * If the wire cannot be inserted 5 * Sequential order for arterial and venous puncture 5 * * Kinked wire 5 * * Punctur...

Objective To evaluate our experience following the introduction of a percutaneous program for endovascular treatment of aortic diseases using Perclose Proglide® assessing efficacy, complications and identification of potential risk factors that could predict failure or major access site complications. Methods A retrospective cohort study during a two-year period was performed. All the patient...

[3] P. B. Callahan, " Optimal parallel all-nearest-neighbors using the well-separated pair decomposition, " in

A subset A of a space X is called regular open if A = IntA, and regular closed if X\A is regular open, or equivalently, if A= IntA. A is called semiopen [16] (resp., preopen [17], semi-preopen [3], b-open [4]) ifA⊂ IntA (resp.,A⊂ IntA,A⊂ IntA ,A⊂ IntA∪ IntA). The concept of a preopen set was introduced in [6] where the term locally dense was used and the concept of a semi-preopen set was introd...