Find in Library

In this paper, the concept of a <i>k</i>-(quasi) pseudo metric is generalized to the <i>L</i>-fuzzy case, called a pointwise <i>k</i>-(quasi) pseudo metric, which is considered to be a map <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>d</mi><mo>:</mo><mi>J</mi><mrow><mo>(</mo><msup><mi>L</mi><mi>X</mi></msup><mo>)</mo></mrow><mo>×</mo><mi>J</mi><mrow><mo>(</mo><msup><mi>L</mi><mi>X</mi></msup><mo>)</mo></mrow><mo>⟶</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo></mrow></mrow></semantics></math></inline-formula> satisfying some conditions. What is more, it is proved that the category of pointwise <i>k</i>-pseudo metric spaces is isomorphic to the category of symmetric pointwise <i>k</i>-remote neighborhood ball spaces. Besides, some <i>L</i>-topological structures induced by a pointwise <i>k</i>-quasi-pseudo metric are obtained, including an <i>L</i>-quasi neighborhood system, an <i>L</i>-topology, an <i>L</i>-closure operator, an <i>L</i>-interior operator, and a pointwise quasi-uniformity.