Results 21 to 30 of about 44 (44)
A note on connectedness in cartesian closed categories
International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 1, Page 101-104, 1997., 1997 Primaxily working in the category of limit spaces and continuous maps we suggest a new concept of connectivity with application in all categories where function space objects satisfy natural exponential laws. In a separate Appendix we motivate the development of a homotopy theory for spaces of real‐valued continuous maps endowed with the structure of ...
Reino Vainio
wiley +1 more source
Generalized totally disconnectedness
International Journal of Mathematics and Mathematical Sciences, Volume 18, Issue 3, Page 485-488, 1995., 1994 In this paper totally disconnectedness is generalized to maximal disconnectedness, which is investigated, and additional properties of totally disconnectedncss and 0‐dimensional are given.
Charles Dorsett
wiley +1 more source
Measures of Lindelof and separability in approach spaces
International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 3, Page 597-606, 1994., 1993 In this paper we introduce the notions of separability and Lindelöf in approach spaces and investigate their behaviour under products and subspaces.
R. Baekeland, R. Lowen
wiley +1 more source
International Journal of Mathematics and Mathematical Sciences, Volume 14, Issue 4, Page 709-714, 1991., 1990 We construct two countable, Hausdorff, almost regular spaces I(S), I(T) having the following properties: (1) Every continuous map of I(S) (resp, I(T)) into every Urysohn space is constant (hence, both spaces are connected). (2) For every point of I(S) (resp.
V. Tzannes
wiley +1 more source
A note on maximally resolvable spaces
International Journal of Mathematics and Mathematical Sciences, Volume 13, Issue 3, Page 513-516, 1990., 1989 A.G. El′kin [1] poses the question as to whether any uncountable cardinal number can be the dispersion character of a Hausdorff maximally resolvable space. In this note we prove that every cardinal number ℵ ≥ ℵ1 can be the dispersion character of a metric (hence, maximally resolvable) connected, locally connected space.
V. Tzannes
wiley +1 more source
Order‐theoretical connectivity
International Journal of Mathematics and Mathematical Sciences, Volume 13, Issue 4, Page 717-720, 1990., 1990 Order‐theoretically connected posets are introduced and applied to create the notion of T‐connectivity in ordered topological spaces. As special cases T‐connectivity contains classical connectivity, order‐connectivity, and link‐connectivity.
T. A. Richmond, R. Vainio
wiley +1 more source
A Characterization of Affine Primal Topological Spaces Induced by Nilpotent Matrices
International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.In this article, we prove that an n × n matrix A is nilpotent if and only if there exists an affine primal topology τ for Rn such that the space Rn,τ is both compact and connected. For τ being an affine primal topology, we mean that τ=U⊂Rn:f−1U⊂U, where f:Rn⟶Rn is a map defined by f(x) = Ax + p, with p∈Rn.
Ebner Pineda +3 more
wiley +1 more source
Peano compactifications and property S metric spaces
International Journal of Mathematics and Mathematical Sciences, Volume 3, Issue 4, Page 695-700, 1980., 1980 Let (X, d) denote a locally connected, connected separable metric space. We say the X is S‐metrizable provided there is a topologically equivalent metric ρ on X such that (X, ρ) has Property S, i.e. for any ϵ > 0, X is the union of finitely many connected sets of ρ‐diameter less than ϵ.
R. F. Dickman Jr.
wiley +1 more source
Connectedness via Primal Topological Spaces With Applications of Primals to Rough Operators
Journal of Mathematics, Volume 2025, Issue 1, 2025.In topology, connectedness provides insight into how a space is “in one piece,” rather than being split into disjoint parts. Its significance can be seen through its various applications, such as understanding the nature of solutions to differential equations, the intermediate value theorem, and attaining a maximum and minimum for continuous real ...
Murad Özkoç +4 more
wiley +1 more source
, 1988 International Journal of Mathematics and Mathematical Sciences, Volume 12, Issue 3, Page 435-440, 1989.
D. Baboolal
wiley +1 more source