III.—Notes concerning the anatomy of certain Rotifers

Concerning a Certain Set of Arrangements

there exists an arrangement in 5 in which a* follows all the Oi with i<k. Such sets Ssurely exist; for example, any set of m arrangements whose terminal elements are 1, 2, • • • , m, respectively, will obviously be ^-suitable for any k^m. The smallest cardinal number N such that there exists a set of N arrangements which is ^-suitable for m will be denoted by N(m, k); this is therefore a well d...

Concerning Certain Solvable Equations with Functional Derivatives.

we use in the second step this Zs/bt' instead of the original as/at the mass will be multiplied by the constant factor and this may-correspond to the change of mass considered in the special relativity theory. 1 Cf. a paper by the -present writer, New York, Trans. Amer. Math. Soc., 27, 1925, January, pp. 106-136. 2 Amsterdam, Proceedings, 202, 1918, pp. 1076-1091. 3 Cf. paper cited under' secti...

Concerning the Spans of Certain Plane Separating Continua

Let X be a plane separating continuum. Suppose C is a convex space contained in a bounded component of R2 − X. It is shown that the span of the boundary of C is a lower bound for both the span and semispan of X. It is also shown that if a span of X is equal to the breadth of X and Y satisfies certain conditions relative to X then that span of X is an upper bound for the corresponding span of Y .

Concerning Certain Problems in the Selection of Microorganisms

Concerning the Separability of Certain Locally Connected Metric Spaces

If a connected metric space S is locally separable, then S is separable. If a connected, locally connected, metric space S is locally peripherally separable, then S is separable. Furthermore if a connected, locally connected, complete metric space S satisfies certain "flatness" conditions, it is known to be separable. These "flatness" conditions are rather strong and involve both im kleinen and...