Results 21 to 30 of about 50 (49)
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
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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
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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
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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
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Journal of Mathematics, Volume 2026, Issue 1, 2026.In this paper, we introduce a novel type of open set, called βθ−I‐open sets, constructed by means of an ideal on a topological space. These sets broaden the classical definition of openness. Employing these ideal‐based generalized open sets, we investigate essential topological properties—including connectedness, hyperconnectedness, and extremal ...
Naeem Nisar Sheikh +3 more
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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
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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.
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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
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, 1988 International Journal of Mathematics and Mathematical Sciences, Volume 12, Issue 3, Page 435-440, 1989.
D. Baboolal
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Computing Connectedness: an exercise in computational topology
, 1998 We reformulate the notion of connectedness for compact metric spaces in a manner that may be implemented computationally. In particular, our techniques can distinguish between sets that are connected; have a finite number of connected components; have ...
E. Bradley +3 more
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