We develop the homotopy theory of Euler characteristic (magnitude) of a category enriched in a monoidal model category. If a monoidal model category V is equipped with an Euler characteristic that is compatible with weak equivalences and fibrations in V, then our Euler characteristic of V-enriched categories is also compatible with weak equivalences and fibrations in the canonical model structu...

Let V be a system of weights on a completely regular Hausdorff space and let B(E) be the topological vector space of all continuous linear operators on a Hausdorff topological vector space E. Let CV0(X,E) and CVb(X,E) be the nonlocally convex weighted spaces of continuous functions. In the present paper, we characterize compact multiplication operators Mψ on CV0 (X,E) ( or CVb(X,E)) induced by ...

In this paper, we investigate the L-fuzzy proximities and the relationships betweenL-fuzzy topologies, L-fuzzy topogenous order and L-fuzzy uniformity. First, we show that the category of-fuzzy topological spaces can be embedded in the category of L-fuzzy quasi-proximity spaces as a coreective full subcategory. Second, we show that the category of L -fuzzy proximity spaces is isomorphic to the ...

The aim of this article is to introduce some basic notions of Topological Quantum Field Theory (TQFT) and to consider a modification of TQFT, applicable to embedded manifolds. After an introduction based around a simple example (Section 1) the notion of a d-dimensional TQFT is defined in category-theoretical terms, as a certain type of functor from a category of d-dimensional cobordisms to the ...

‎This paper develops a basic theory of $H$-groups‎. ‎We‎ ‎introduce a special quotient of $H$-groups and‎ ‎extend some algebraic constructions of topological groups to the category‎ ‎of H-groups and H-maps and then present a functor from this category to the category of quasitopological groups‎.

We prove that every homogeneous countable dense topological space containing a copy of the Cantor set is Baire space. In particular, vector It follows that, for any nondiscrete metrizable X X</mml:an...

Starting with the motivating example of Stone’s representation theorem that allows one to represent Boolean algebras as subalgebras of the poweralgebra of a sufficiently large set, we ask the question of whether it is possible to generalize this to a relationship between lattice theory and topology. This can be done by considering special lattices called locales, which are, in a sense, a suitab...

The branching space of a flow is the topological space of germs of its nonconstant execution paths beginning in the same way. However, there exist weakly Shomotopy equivalent flows having non weakly homotopy equivalent branching spaces. This topological space is then badly behaved from a computer-scientific viewpoint since weakly S-homotopy equivalent flows must correspond to higher dimensional...

The signature of the Poincaré duality of compact topological manifolds with local system of coefficients can be described as a natural invariant of nondegenerate symmetric quadratic forms defined on a category of infinite dimensional linear spaces. The objects of this category are linear spaces of the form W = V ⊕ V ∗ where V is abstarct linear space with countable base. The space W is consider...