In this paper we identify the “nil-terms” for Waldhausen’s algebraic K-theory of spaces functor as the reduced K-theory of a category of equivariant spaces equipped with a homotopically nilpotent endomorphism.

Generalising Nachbin's theory of ``topology and order'', in this paper we   continue the study of quantale-enriched categories equipped with a compact   Hausdorff topology. We compare these $V$-categorical compact Hausdorff spaces   with ultrafilter-quantale-enriched categories, and show that the presence of a   compact Hausdorff topology guarantees Cauchy completeness and (suitably   defined) ...

We prove an adjoint functor theorem in the setting of categories enriched a monoidal model category $\mathcal V$ admitting certain limits. When is equipped with trivial structure this recaptures version Freyd's theorem. For non-trivial structures, we obtain new theorems homotopical flavour - particular, when simplical sets appropriate to $\infty$-cosmoi Riehl and Verity. also investigate access...

A link in the 3−sphere is homotopically trivial, according to Milnor, if its components bound disjoint maps of disks in the 4−ball. This paper concerns the question of what spaces give rise to the same class of homotopically trivial links when used in place of disks in the analogous definition. We show that there are 4−manifolds for which this property depends on their embedding in the 4−ball. ...

In this paper, the Urysohn, completely Hausdorff and completely regular axioms in $L$-topological spaces are generalized to $L$-fuzzy topological spaces. Each $L$-fuzzy topological space can be regarded to be Urysohn, completely Hausdorff and completely regular tosome degree. Some properties of them are investigated. The relations among them and $T_2$ in $L$-fuzzy topological spaces are discussed.

In this paper we identify the “nil-terms” for Waldhausen’s algebraic K-theory of spaces functor as the reduced Ktheory of a category of equivariant spaces equipped with a homotopically nilpotent endomorphism.