Minimal usco and minimal cusco maps and the topology of pointwise convergence
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Dušan Holý
Abstract
Let X be a Hausdorff topological space, MU(X, ℝ) and MC(X, ℝ) be the space of all minimal usco maps with values in ℝ and the space of all minimal cusco maps with values in ℝ, respectively. By τp is denoted the topology of pointwise convergence. We characterize some cardinal invariants of (MU(X, ℝ), τp) and (MC(ℝ,ℝ), τp). Let Q(ℝ,ℝ) be the space of all quasicontinuous functions on ℝ with values in ℝ and C(ℝ,ℝ) the space of all continuous functions on ℝ with values in ℝ. We compare cardinal invariants of (MU(ℝ,ℝ), τp), (MC(ℝ,ℝ), τp), (Q(ℝ,ℝ), τp) and (C(ℝ,ℝ), τp).
(Communicated by David Buhagiar)
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Articles in the same Issue
- A note on the coprime power graph of groups
- Simplified axiomatic system of DRl-semigroups
- Special filters in bounded lattices
- Reichenbach’s causal completeness of quantum probability spaces
- A construction of magmas and related representation
- Extensions of the triangular D(3)-Pair {3, 6}
- Hermite-Hadamard type inequalities for new class h-convex mappings utilizing weighted generalized fractional integrals
- Divergence operator of regular mappings
- Monotonicity of the ratio of two arbitrary gaussian hypergeometric functions
- Oscillation and asymptotic criteria for certain third-order neutral differential equations involving distributed deviating arguments
- Multiplicity results for a fourth-order elliptic equation of p(x)-kirchhoff type with weights
- Singular discrete dirac equations
- Convergence of bivariate exponential sampling series in logarithmic weighted spaces of functions
- Fundamental inequalities for the iterated Fourier-cosine convolution with Gaussian weight and its application
- Existence of solutions and Hyers-Ulam stability for κ-fractional iterative differential equations
- On almost cosymplectic generalized (k, μ)ʹ-spaces
- On some recent selective properties involving networks
- Minimal usco and minimal cusco maps and the topology of pointwise convergence
- Corrigendum to: Every positive integer is a sum of at most n + 2 centered n-gonal numbers
