The metrizability of sprays, particularly symmetric linear connections, is studied in terms of semi-basic 1-forms using the tools developed by Bucataru and Dahl in [2]. We introduce a type of metrizability in relationship with the Finsler and projective metrizability. The Lagrangian corresponding to the Finsler metrizability as well as the Bucataru–Dahl characterization of Finsler and projectiv...

The notion of a regular operator with compact supports between function spaces is introduced. On that base we obtain a characterization of absolute extensors for 0-dimensional spaces in terms of regular extension operators having compact supports. Milyutin maps are also considered and it is established that some topological properties, like paracompactness, metrizability and k-metrizability, ar...

An algebraic notion of representational consistency is defined. A theorem relating it to free actions is proved. A metrizability problem of the quotient (a shape space) is discussed. This leads to a new algebraic variety with a metrizability result. A concrete example is given from stereo vision.

In this essentially selfcontained paper first we establish an intrinsic version and present a coordinate-free deduction of the so-called Rapcsák equations, which provide, in the form of 2nd order PDE-s, necessary and sufficient conditions for a Finsler structure to be projectively related to a spray. From another viewpoint, the Rapcsák equations are the conditions for the Finsler-metrizability ...

Every Finsler metric naturally induces a spray but not so for the converse. The notion sprays of scalar (resp. isotropic) curvature has been known as generalization metrics flag curvature. In this paper, new notion, constant curvature, is introduced and especially it shows that isotropic necessarily even in dimension $$n\ge 3$$ . Further, complete conditions are given constant) to be metrizable...

The main purpose of this paper is to prove the metrizability of semi-aposyndetic continuum X which admits a Whitney map for C(X).

We consider the topological structure of sublinear quasi-metrics in locally convex cones and define notion a quasi-metric cone. The presence upper bounded neighborhoods, gives necessary sufficient conditions for quasi-metrizability cones. In particular, we investigate boundedness separatedness characterize metrizability

Two generalized uniform structures namely fuzzy quasi-uniformity and fuzzy local quasi-uniformity are introduced. Conditions of fuzzy quasi-uniformizability and quasi-metrizability are examined. Mathematics Subject Classification: 54E15, 54A20