A Novel Fuzzy Structure: Infra-Fuzzy Topological Spaces

Obtaining a weaker condition that preserves some inspired topological properties is always desirable. As result, we introduce the concept of infra-fuzzy topology, which subset family degrades fuzzy topology by omitting closedness under arbitrary unions. Fundamental spaces are investigated, including open and closed sets, interior closure operators, boundary set. It not possible to expect latter concepts have identical those in ordinary spaces. More precisely, set need be open, may closed. Then, employing neighborhood systems, Q-neighborhood basis relative propose several approaches for generating topologies. Finally, define notions continuity, openness, closedness, homeomorphism mappings context infra fuzziness investigate their characterizations. We show usual characterization earlier structure incorrect. demonstrate all homeomorphisms on an space forms group composition. finish this work proving each between two produces isomorphism groups corresponding