Compactness and compactifications in generalized topology

Compactness in Topology and Computation

Compactness in locales and in formal topology

If a locale is presented by a “flat site”, it is shown how its frame can be presented by generators and relations as a dcpo. A necessary and sufficient condition is derived for compactness of the locale (and also for its openness). Although its derivation uses impredicative constructions, it is also shown predicatively using the inductive generation of formal topologies. A predicative proof of ...

Compactness of Lim-inf Topology

L {inf B; B ranges over subsets of L: B ∈ F}. One can prove the following proposition (1) Let L1, L2 be complete lattices. Suppose the relational structure of L1 = the relational structure of L2. Let X1 be a non empty subset of L1, X2 be a non empty subset of L2, F1 be a filter of 2 X1 ⊆ , and F2 be a filter of 2 X2 ⊆ . If F1 = F2, then lim inf F1 = lim inf F2. Let L be a non empty FR-structure...

Nonstandard Analysis in Topology: Nonstandard and Standard Compactifications

Let (X,T ) be a topological space, and X a non–standard extension of X . There is a natural “standard” topology T on X generated by G, where G ∈ T . The topological space ( X, T ) will be used to study, in a systematic way, compactifications of (X,T ) . Mathematics Subject Classification: 031105, 54J05, 54D35, 54D60.

Mirror Symmetry in Generalized Calabi–Yau Compactifications

We discuss mirror symmetry in generalized Calabi–Yau compactifications of type II string theories with background NS fluxes. Starting from type IIB compactified on Calabi– Yau threefolds with NS three-form flux we show that the mirror type IIA theory arises from a purely geometrical compactification on a different class of six-manifolds. These mirror manifolds have SU(3) structure and are terme...