A strong shape theory admitting an S-dual

A strong shape theory with S-duality

If in the classical S-category P, 1) continuous mappings are replaced by compact-open strong shape (= coss) morphisms (cf. §1 or [1], §2), and 2) ∧-products are properly reinterpreted, then an S-duality theorem for arbitrary subsets X ⊂ S (rather than for compact polyhedra) holds (Theorem 2.1). 0. Introduction. In a previous paper [1] we introduced the concept of coss-shape (compact-open strong...

A functional S-dual in a strong shape category

In the S-category P (with compact-open strong shape mappings, cf. §1, instead of continuous mappings, and arbitrary finite-dimensional separable metrizable spaces instead of finite polyhedra) there exists according to [1], [2] an S-duality. The S-dual DX, X = (X,n) ∈ P, turns out to be of the same weak homotopy type as an appropriately defined functional dual (S0)X (Corollary 4.9). Sometimes th...

Black holes admitting a Freudenthal dual

The quantised charges x of four dimensional stringy black holes may be assigned to elements of an integral Freudenthal triple system whose automorphism group is the corresponding U-duality and whose U-invariant quartic norm ∆(x) determines the lowest order entropy. Here we introduce a Freudenthal duality x→ x̃, for which ̃̃ x = −x. Although distinct from U-duality it nevertheless leaves ∆(x) inva...

Ergodic Theory of Markov Chains Admitting an Infinite Invariant Measure.

a generalization of strong causality

در این رساله t_n - علیت قوی تعریف می شود. این رده ها در جدول علیت فضا- زمان بین علیت پایدار و علیت قوی قرار دارند. یک قضیه برای رده بندی آنها ثابت می شود و t_n- علیت قوی با رده های علی کارتر مقایسه می شود. همچنین ثابت می شود که علیت فشرده پایدار از t_n - علیت قوی نتیجه می شود. بعلاوه به بررسی رابطه نظریه دامنه ها با نسبیت عام می پردازیم و ثابت می کنیم که نوع خاصی از فضا- زمان های علی پایدار, ب...