Quasi Locally Connected Spaces and PseudoLocally Connected Spaces

摘要

Two new generalizations of locally connected spaces called `quasi locallyconnected spaces' and `pseudo locally connected spaces' are introduced and their ba-sic properties are studied. The class of quasi locally connected spaces properly con-tains the class of almost locally connected spaces (J. Austral. Math. Soc. 31(1981),421-428) and is strictly contained in the class of pseudo locally connected spaceswhich in its turn is properly contained in the class of sum connected spaces (Math.Nachrichten 82(1978), 121-129; Ann. Acad. Sci. Fenn. A I Math. 3(1977), 185-205).Product and subspace theorems for quasi (pseudo) locally connected spaces are di-scussed. Their preservation under mappings and their interplay with mappings areoutlined. Function spaces of quasi (pseudo) locally connected spaces are considered.Change of topology of a quasi (pseudo) locally connected space is considered so thatit is simply a locally connected space in the coarser topology. In contradistinctionwith almost locally connected spaces, quasi (pseudo) locally connected spaces con-stitute a coreflective subcategory of TOP.