It is shown that every metrizable consonant space is a Cantor set-selector. Some applications are derived from this fact, also the relationship is discussed in the framework of hyperspaces and Prohorov spaces.
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We present a few results and problems related to spaces of continuous functions with the topology of pointwise convergence and the classes of LΣ(≤ ω)-spaces; in particular, we prove that every Gul’ko compact space of cardinality less or equal to $$ \mathfrak{c} $$ is an LΣ(≤ ω)-space.
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Certain properties of homotopies of admissible multivalued mappings shall be presented, along with their applications as the tool for examining the acyclicity of a space.
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In this paper a class of general type α-admissible contraction mappings on quasi-b-metric-like spaces are defined. Existence and uniqueness of fixed points for this class of mappings is discussed and the results are applied to Ulam stability problems. Various consequences of the main results are obtained and illustrative examples are presented.
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The purpose of this article is to present fixed point results for multivalued E ≤-contractions on ordered complete gauge space. Our theorems generalize and extend some recent results given in M. Frigon [7], S. Reich [12], I.A. Rus and A. Petruşel [15] and I.A. Rus et al. [16].
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Let X be an infinite, locally connected, locally compact separable metrizable space. The space C(X) of real-valued continuous functions defined on X with the compact-open topology is a separable Fréchet space, so it is homeomorphic to the psuedo-interior s = (−1, 1)ℕ of the Hilbert cube Q = [−1, 1]ℕ. In this paper, generalizing the Sakai-Uehara’s result to the non-compact case, we construct a natural compactification $$ \bar C $$(X) of C(X) such that the pair ($$ \bar C $$(X), C(X)) is homeomorphic to (Q, s). In case X has no isolated points, this compactification $$ \bar C $$(X) coincides with the space USCCF(X,) of all upper semi-continuous set-valued functions φ: X → = [−∞, ∞] such that each φ(x) is a closed interval, where the topology for USCCF(X, ) is inherited from the Fell hyperspace Cld*F(X × ) of all closed sets in X × .
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In this paper, the authors prove some existence results of solutions for a new class of generalized bi-quasi-variational inequalities (GBQVI) for quasi-pseudo-monotone type II and strongly quasi-pseudo-monotone type II operators defined on compact sets in locally convex Hausdorff topological vector spaces. In obtaining these results on GBQVI for quasi-pseudo-monotone type II and strongly quasi-pseudo-monotone type II operators, we shall use Chowdhury and Tan’s generalized version [3] of Ky Fan’s minimax inequality [7] as the main tool.
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We construct a cohomological index of the Fuller type for set-valued flows in normed linear spaces satisfying the properties of existence, excision, additivity, homotopy and topological invariance. In particular, the constructed index detects periodic orbits and stationary points of set-valued dynamical systems, i.e., those generated by differential inclusions. The basic methods to calculate the index are also presented.
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