SPECIAL REFERENCE CHARTS

The next few pages contain six basic reference charts which display the properties of the various examples. The properties of a topological space have been grouped into six nearly disjoint categories: separation, compactness, paracompactness, connectedness, disconnectedness, and metriza-tion. In each category we have listed those spaces whose behavior is particularly appropriate. We usually chose any space which represented a counterexample in that category or which exhibited either an unusual or an instructive pathology; occasionally we listed a space simply because it was so well behaved.

Entries in the charts are either 1, 0, or -, meaning, respectively, that the space has the property, does not have the property, or that the property is inapplicable. Occasional blanks represent properties which were not discussed in the text and which do not appear to follow simply from anything that was discussed. Examples are listed by number, and in a few cases the tables extend beyond one page in length.

Table I

SEPARATION AXIOM CHART

Table II

COMPACTNESS CHART

Table III

PARACOMPACTNESS CHART

Table IV

CONNECTEDNESS CHART

Table V

DISCONNECTEDNESS CHART

Table VI

METRIZABILITY CHART