Scientists apply digital computers to perform computations on natural numbers, nite strings, real numbers and more general objects like sets, functions and measures. While computability theory on many countable sets is well established and for computability on the real numbers several (unfortunately mutually non-equivalent) deenitions are being studied, in particular for measures no computabili...

The following figure (adapted from [1]) shows the abstract view of the SMFFC topology with g m f 1 = 0, we note that it is equivalent to the SMC topology in this case:

A topology on a lattice L or more generally on a partially ordered set P is called an intrinsic topology if it is de ned directly from the order Early ex amples of such topologies were the interval topology of O Frink Fr and the order topology introduced by G Birkho Bi The early intrinsic topolo gies were typically symmetric i e the topology de ned on L agreed with the topology de ned on L the ...

Structural topology plays an important role in protein mechanical stability. Proteins with β-sandwich topology consisting of Greek key structural motifs, for example, I27 of muscle titin and (10)FNIII of fibronectin, are mechanically resistant as shown by single-molecule force spectroscopy (SMFS). In proteins with β-sandwich topology, if the terminal strands are directly connected by backbone H...

in this paper we investigate generalized topologies generated by a subbase ofpreorder relators and consider its application in the concept of the complement. we introducethe notion of principal generalized topologies obtained from the new type of open sets andstudy some of their important properties.

which is part of a certain 2d Hamiltonian cohomological field theory [11]. Here we use this map to study the topology of ΩHam(M, ω) and its Hofer geometric properties via a kind of virtual Morse theory for the positive Hofer length functional, L : ΩHam(M, ω) → R . We also use Ψ to prove a kind of index theorem for some critical points of L . We apply this theory to get some concrete application...