In this paper we study the conditions under which a fuzzy topological space becomes a fuzzy almost resolvable space and the inter-relations between fuzzy almost resolvable, fuzzy almost irresolvable spaces, fuzzy submaximal spaces, fuzzy first category spaces, fuzzy Baire spaces, fuzzy weakly Volterra spaces are also investigated.

We study a class of equilibrium problems which is identified with a complete metric space of functions. For most elements of this space of functions in the sense of Baire category, we establish that the corresponding equilibrium problem possesses a unique solution and is well-posed.

Abstract Given a cofinal cardinal function $h\in {}^{\kappa }\kappa $ for $\kappa inaccessible, we consider the dominating h -localisation number, that is, least cardinality of set -slaloms such every -real is localised by slalom in set. It was proved [3] localisation numbers can be consistently different two functions (the identity and power function). We will construct ^+$ -sized family their...

In ZF (i.e., Zermelo-Fraenkel set theory without the Axiom of Choice) the following statements are shown to be equivalent: (1) The axiom of dependent choice. (2) Products of compact Hausdorff spaces are Baire. (3) Products of pseudocompact spaces are Baire. (4) Products of countably compact, regular spaces are Baire. (5) Products of regular-closed spaces are Baire. (6) Products of Čech-complete...

This paper studies how well computable functions can be approximated by their Fourier series. To this end, we equip the space of L-computable functions (computable Lebesgue integrable functions) with a size notion, by introducing L-computable Baire categories. We show that L-computable Baire categories satisfy the following three basic properties. Singleton sets {f} (where f is L-computable) ar...

This paper studies how well computable functions can be approximated by their Fourier series. To this end, we equip the space of L-computable functions (computable Lebesgue integrable functions) with a size notion, by introducing L-computable Baire categories. We show that L-computable Baire categories satisfy the following three basic properties. Singleton sets {f} (where f is L-computable) ar...

Let E be a completely regular topological space. Mitoma [9 ], extending the classical case E = R 1, has recently introduced the Skorokhod topology on the space D( [0, 1 ] : E). This topology is investigated in detail. We find families of continuous functions which generate the topology, examine the structure of the Borel and Baire a-algebras of D( [0, 1 ] : E) and prove tightness criteria for E...

Every computable function has to be continuous. To develop computability theory of discontinuous functions, we study low levels of the arithmetical hierarchy of nonuniformly computable functions on Baire space. First, we classify nonuniformly computable functions on Baire space from the viewpoint of learning theory and piecewise computability. For instance, we show that mind-change-bounded-lear...

$C_{p}\left ( X\right )$ is distinguished $\Leftrightarrow$ the strong dual $L_{\beta }\left barrelled bidual $M\left ) =\mathbb {R}^{X}$. So one may judge how nearly by is, and also near dense subspace to Baire space $\mathbb Being Baire-like, always fairly close {R}^{X}$ in that sense. But if not distinguished, we show codimension of uncountable, i.e., algebraically far from {R}^{X}$, moreove...