A sequence of convex sets

"Dr. Chantal," wondered Bob, turning from the board for a moment, "could you use Brouwer’s theorem to show that if m doesn't equal n then M and N can't be homeomorphic?" Kate grinned. "Absolutely. Can anyone state Brouwer's theorem?"

When Kate had first appeared to teach the topology seminar, listed under Mielke's name, they had hovered uncomfortably in the hallway, waiting for the woman camped out in their seminar room to get herself sorted and leave. When she finally came out and inquired if there were waiting for Math 637, they wondered if she was the new departmental secretary, come to tell them that the class had moved.

She had introduced herself as Kathryn Chantal and explained that Prof. Mielke was serving as interim dean, but had asked her to fill in. As she began to write the syllabus on the board, Bob had leaned over to Mike and whisphered meant to be overheard, "How gullible does Mielke think we are? K. Chantal? As in Chantal's selection theorem? I've got half a mind to march down and call him on it." Mike elbowed him. "Wanna come?" Mike pointed.

Kate had given over the syllabus and begun writing a proof on the board. Given a sequence {Kn} of convex sets contained in a bounded set...

Fifteen minutes later, without saying a word, she had covered the board from top left to bottom right, finishing with one line: Therefore a metric space of convex bodies is locally compact. K. Chantal, Trans. Am. Math. Soc. 87, 369 (1953).

"My doctoral work. How gullible are you, Mr. Andrews?" Mike blushed and even Bob had the grace to look chagrined.

Suburban Demimonde

"She's going again, I saw the cab pick her up," Martha's caller gasped.

"I saw. Gloves. I haven't seen her wear gloves since last Easter. And that sister's station wagon is parked in the driveway again."

Martha's attempts to wring from Diana any information on the whereabouts of Kate had been met by Diana with a hot coffee, fresh crumb cake and cheerful barrage of anecdotes about the children, but no particulars regarding her sister whatsoever. Diana was clearly an expert in the Cold War politics of the surburban wives' demimonde.

It really wasn't about Kate, but about Harry. They all felt just a bit protective of Harry, who had held them all at arm's length during high school, and those long college summers. When he returned to practice law, they wondered who would be Mrs. Doughtery. Would he bring home a sweetheart?

A decade later, despite innumerable dinner parties where cousins and younger sisters were paraded past, Harry remained single. Martha found the memories of the day Harry interrupted her as she gushed over her cousin, "with a degree from Barnard last year, you know?" still rankled. "I'm certain she's charming," Harry said, "but I am engaged." She still wasn't sure if it was the fact that Harry had chosen someone from so far away — Philadelphia. Or so old. Or just that she hadn't had the smallest inkling.

Red flags

"Good afternoon, Mrs. Dougherty," says the conductor with a grin as he hoists Kate's battered bag up from the platform.  Kate is a regular on this train, picking it up every Monday since September.  Tim slides the bag in the rack over a foursome of empty seats and heads off down the aisle, swaying as the train lumbers out of the station.

She pulls out a stack of papers from Harry's old law school bag, and digs in the bottom for a red pencil.  No matter how often she replenishes them,  she nevers seems to be able to find more than one at any given moment.  Ah, there, at the very bottom, huddled between her lipstick and a bottle of St. Joseph baby aspirin.  The teeth marks made it clear this one had been around the block at least once with Patty.  

Is this a red flag?  Kate is worried about her eldest.  At the cusp of adolescence, an unsettling time for anyone, but for Patty — oh, for Patty, who has her life flipped like an eggtimer every four years, will the sand come spilling out at this this turn of events?  Emma has been reassuring, but Kate sometimes wonders what her Patricia's serene exterior conceals.

A cup of coffee appears at her elbow, jolting her back to her grading.  She grins at Tim and digs in. Six hours to Chicago, six blessedly undisturbed hours....

Decision trees and Disney princesses

The cab driver stood uneasily, shifting from foot to foot as she hugged Diana in the hallway.  

"Di, I can't tell you how I appreciate this."  

"Go.  It's good for me.  Honestly, a couple of days with Charlie and the gang and teenagers start to look easy again!"

Di's ninth and youngest was still at home, in all likelihood reveling in the chance to sit down with his father in the basement with a pizza and the Black Hawks game and no need to carry on a conversation.

Kate handed off her suitcase to the cabbie and Charles to Di and let the storm door slam behind her.  In the cab, she pulled on her gloves.  Good, she would be early for the train.  She hated the tension of running behind schedule, her mind running through an ever expanding set of possibilities: if she missed the 11:42, would there be a seat on the 12:15? and could she get in touch with Mielke before he left the university for the station? The decision tree branched in her head like the vines in a Disney cartoon, intent on tying the princess down.  She breathed in the sudden spaciousness and leaned back against the seat.

Eyes closed, she didn't notice the kitchen curtains flicking aside as the cab headed down the hill. The first phone was ringing before the cab hit the stop sign by the elementary school.

Inelastic time

It's after midnight, Harry's snores are tumbling down the stairs, and even the cat has rolled herself up for the night.  How much longer before the tenacles of sleep wrap themselves around her, dragging her head down to the table? 

Kate glances at the clock.  Ten more minutes until that last load of laundry is dry, and she can crawl into bed.  She scrawls one more note on the pad, tears off the sheets and tacks them firmly to the bulletin board in the kitchen. 

She gathers herself up and heads to the basement.  With luck, Diana won't need to deal with the diapers before she gets back.  Her sister has more than done her time on diaper detail.  She folds the last diaper and tucks them into the basket.

Her suitcase is packed and hidden in the closet near the front door, the tickets to Chicago tucked in her purse along with the one pair of matching white gloves she could find.  Sleep is the only thing left on the list to tick off.  One a.m.?  Oh God, five hours just isn't enough.  She can hear John's sigh now,  "Time is not infinitely elastic, Kate. It's not like one of your surfaces."

On Mulberry Street

Its cord stretched the length of the tiny kitchen, she cradled the phone behind her ear and listened to the breathless voice detail the outfits to be modeled at the upcoming parish fashion show.  She absent-mindedly scraped a bit of applesauce off Charles' chin and popped it back into his mouth.

"I'm happy to wear whatever you think best, Martha" she slid into the gap between evening wear and bridal gowns.  Frankly, the only evening wear she coveted these days was a thick down comforter, and when it came to bridal gowns, she already had two neatly packed away in the back of the closet.  "Keepsake for your daughter" the boxes advertised in looping white script, though she'd never wish the need for a second on her oldest.

Charles squirmed as she wiped his face and plopped him onto the floor, where he promptly headed straight for the window, pressing both hands and nose flat against the glass, waiting for who knew what to come down the quiet street.  Maybe Patty had read him To Think that I saw it on Mulberry Street one too many times?  

"Just let me know what sort of shoes to bring and I'll be there."  

"Yes, yes, mmm, yes.  Bye." Click.  Martha vanished from her consciouness like a burst soap buble.

She breathed in the silence, dropped the spoon into the soapy water in the sink, and wiped her hands on the dishtowel tied around her waist.  Sliding open the drawer nearest the stove, she pulled out a lined yellow pad.  Lines curled around the page, like so many doodles.  Could she steal a few minutes?